Physics Exam 2 Questions and Answers With hints SCORE an A (2025 Version).

Physics Exam 2 Questions and Answers With hints SCORE an A (2025 Version). A 1200-N crate rests on the floor. How much work is required to move it at constant speed: a) 5.0 m along the floor against a friction force of 230 N? b) 5.0 m vertically? (Ch 6 - #4) a) 1150 J = 1200 J b) 6000 J What is the minimum work needed to push a 950-kg car 710 m up along a 9.0 degree incline? Ignore friction. (Ch 6 - #5) 1.0 x 10^6 J A 380-kg piano slides 2.9 m down a 25 degree incline and is kept from acceleration by a man who is pushing back on it parallel to the incline. Determine: a) the force exerted by the man b) the work done on the piano by the man c) the work done on the piano by the force of gravity d) the net work done on the piano Ignore friction. (Ch 6 - #10) a) 1600 N b) -4600 J c) 4600 J d) 0 a) If the kinetic energy of a particle is tripled, by what factor has its speed increased? b) If the speed of a particle is halved, by what factor does its kinetic energy change? (Ch 6 - #16) a) square root 3 b) speed will change by a factor of 1/4 An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow? (Ch 6 - #21) 43 m/s Hint: The force exerted is being completely changed into kinetic energy. Fd = W = KE2 - KE1 If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver's reaction time. (Ch 6 - #22) 2.25 A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high. a) What is the hiker's change in potential energy? b) What is the minimum work required of the hiker? c) Can the actual work done be greater than this? (Ch 6 - #29) a) 9.06 x 10^5 J b) 9.06 x 10^5 J c) Yes, the force of friction would require more work to overcome. In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of 0.50 m/s? (Ch 6 - #34) 6.4 m/s Hint: KE+ PE = KE + PE A 1200-kg car moving on a horizontal surface has speed v= 85 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring? (Ch 6 - #37) 1.4 x 10^5 N/m Hint: KE + KEspring = KE + KEspring A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of 4.5 m/s. a) How fast is he going as he lands on the trampoline, 2.0 m below? b) If the trampoline behaves like a spring of spring constant 5.8 x 10^4 N/m, how far down does he depress it? (Ch 6 - #38) a) 7.7 m/s b) 0.26 m Hint: a) E1 = E2 KE + PE = KE + PE b) E2 = E3 KE + PE + KEspring = KE + PE + KEspring A vertical spring, whose spring constant is 875 N/m, is attached to a table and is compressed down by 0.160 m. a) What upward speed can it give to a 0.380-kg ball when released? b) How high above its original position (spring compressed) will the ball fly? (Ch 6 - #39) a) 7.47 m/s b) 3.01 m Hint: a) KE + PE + KEspring = KE + PE + KEspring b) KE + PE + KEspring = KE + PE + KEspring Finding y2-y1, not just y1 A rollar-coaster car is pulled up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2,3, and 4. Peak 1 = 32 m up Peak 2 = 0 m (lowest point of coaster) Peak 3 = 26 m up Peak 4 = 14 m up (Ch 6 - #40) Peak 2 = 25 m/s Peak 3 = 11 m/s Peak 4 = 19 m/2 Hint: All answers relative to Peak 1 What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 4.0 g? (Ch 6 - #42) k = 2600 N/m Hint: 1) KE = KE spring (solve for x) 2) F= ma = -kx 3) Substitute x from part 1 4) Solve for k A 16.0-kg child descends a slide 2.20 m high and, starting from rest, reaches the bottom with a speed of 1.25 m/s. How much thermal energy due to friction was generated in this process? (Ch 6 - #47) 332 J You drop a ball from a height of 2.0 m, and it bounces back to a height of 1.6 m. a) What fraction of its initial energy is lost during the bounce? b) What is the ball's speed just before and just after the bounce? c) Where did the energy go? (Ch 6 - #52) a) 20% b) 6.3 m/s (before), 5.6 m/s (after) c) The energy was lost as heat. Hint: a) (y1-y2)/y1 b) The height is now 1.6 because it started from 0, not 2.0 m. If a car generates 18 hp when traveling at a steady 95 km/h, what must be the average force exerted on the car due to friction and air resistance? (Ch 6 - #60) F = 510 N Hint: Power= Fv 746 W/1 Hp A shot-putter accelerates a 7.3-kg shot from rest to 14 m/s in 1.5 s. What average power was developed? (Ch 6 - #62) 480 W Hint: Think about the energy being used... what is happening in the problem to the shot? During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33 degree angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance. (Ch 6 - #66) 480 W Hint: The question is asking for on the way up! How high will a 1.85-kg rock go from the point of release if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance. (Ch 6 - #74) 4.41 m Electric energy units are often expressed in "kilowatt-hours." a) Show that one kilowatt-hour (kWh) is equal to 3.6 x 10^6 J. b) If a typical family of four uses electric energy at an average rate of 580 W, how many kWh would their electric bill show for one month? c) And, how many joules would this be? d) At a cost of $0.12 per kWh, what would their monthly bill be in dollars? Does their monthly bill depend on the rate at which they use the electric energy? (Ch 6 - #87) a) See homework b) 420 kWh c) 1.5 x 10^9 J d) $50 - No because the energy measured is not of the power of energy used but is the measure of all the energy. A ball is attached to a horizontal cord of length (l) whose other end is fixed. a) If the ball is released, what will be its speed at the lowest point of its path? b) A peg is located a distance (h) directly below the point of attachment of the cord. If h=0.80l, what will be the speed of the ball when it reaches the top of its circular path about the peg? (Ch 6 - #90) a) v = (square root) 2gl b) v = (square root) 1.2gl Hint: a) PE = KE b) PE2 + KE2 = PE3 + KE3 A 110-kg tackler moving at 2.5 m/s meets head on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after collision? (Ch 7 - #4) 0.70 m/s Hint: Watch the direction of the objects moving toward each other! Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of 1300 kg/s with a speed of 4.5 x 10^4 m/s. (Ch 7 - #5) 5.9 x 10^7 N in the opposite direction of the velocity of the gas A 7700-kg boxcar traveling 14 m/s strikes a second car at rest. The two stick together and move off with a speed of 5.0 m/s. What is the mass of the second car? (Ch 7 - #6) m2 = 13860 kg = 14000 kg A child in a boat throws a 5.30-kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and the mass of the boat is 35.0 kg. (Ch 7 - #7) -0.898 m/s Hint: Initial velocity is zero A 725-kg two stage rocket is traveling at a speed of 6.60 x 10^3 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.80 x 10^3 m/s relative to each other along the original line of motion. a) What is the speed and direction of each section (relative to Earth) after the explosion? b) How much energy was supplied by the explosion? (Ch 7 - #14) a) 8.00 x 10^3 m/s away from earth; 5.20 x 10^3 m/s away from earth b) 7.11 x 10^8 J A 12-kg hammer strikes a nail at a velocity of 7.5 m/s and comes to rest in a time interval of 8.0 milliseconds. a) What is the impulse given to the nail? b) What is the average force acting on the nail? (Ch 7 - #17) a) 90 kg m/s b) 11000 N A tennis ball of mass 0.060 kg and speed of 28 m/s strikes a wall at a 45 degree angle and rebounds with the same speed at 45 degrees. What is the impulse (magnitude and direction) given to the ball? (Ch 7 - #18) 2.4 kg m/s to the left Hint: When a ball bounces off the wall, is it moving horizontally or vertically? A 95-kg fullback is running at 3.0 m/s to the east and is stopped in 0.85 s by a head-on tackle by a tackler running due west. a) Calculate the original momentum of the fullback b) The impulse exerted on the fullback c) The impulse exerted on the tackler d) The average force exerted on the tackler (Ch 7 - #21) a) 285 kg m/s to the east b) -285 kg m/s c) 285 kg m/s to the east d) 340 N to the east Hint: b) Impulse = ΔP (momentum) d) FΔt = ΔP A ball of mass 0.440 kg moving east with a speed of 3.80 m/s collides head-on with a 0.220 kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision? (Ch 7 - #25) Va' = 1.27 m/s east Vb' = 5.07 m/s east Hint: Va - Vb = - (Va' - Vb') A ball of mass 0.220 kg that is moving with a speed of 5.5 m/s collides head-on elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a speed of 3.8 m/s. a) Calculate the velocity of the target ball after the collision b) The mass of the target ball (Ch 7 - #31) a) 1.7 m/s b) 1.2 kg Hint: a) Va - Vb = -(Va' - Vb') A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's maximum displacement. (Ch 7 - #35) h = 0.15 m v = 0.90 m A 980-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact. What was that speed? (Ch 7 - #37) 21 m/s Hint: Use substitution! Will have to find our two ways in which to find force/work done and equal them together and then solve A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse it lit. When the firecracker explodes inside, the two blocks separate and slide apart. What is the ratio of distances each block travels? (Ch 7 - #40) 1/9 A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of 9.6 x 10^-23 kg m/s and 6.2 x 10^-23 kg m/s. Determine the magnitude and the direction of the momentum of the second (recoiling) nucleus. (Ch 7 - #45) 147 degrees from the electron's momentum 123 degrees from the neutrino's momentum Find the center of mass of the three-mass system shown relative to the 1.00-kg mass. 1.00 kg 1.50 kg 1.10 kg (0.50m) (0.25m) (Ch 7 - #50) 0.438 m Three cubes, of side lo, 2lo, 3lo, are placed next to one another (in contact) with their centers along a straight line. What is the position, along the line, of the CM of this system? (Ch 7 - #52) 3.8 lo from left edge of smallest cub The masses of the Earth and Moon are 5.98 x 10^24 kg and 7.35 x 10^22 kg, respectively, and their centers are separated by 3.84 x 10^8 m. a) Where is the CM of the Earth-Moon system located? b) What can you say about the motion of the Earth-Moon system about the Sun, and of the Earth and Moon separately by the Sun? (Ch 7 - #61) a) 4.66 x 10^6 from center of Earth b) A mallet consists of a uniform cylindrical head of mass 2.30 kg and a diameter 8.00 cm mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory? (Ch 7 - #62) 25.1 cm Hint: Find cm using the mallet bottom as the reference A meteor whose mass was about 1.5 x 10^8 kg struck the Earth (m= 6.0 x 10^24 kg) with a speed of about 25 km/s and came to rest in the Earth. a) What was the Earth's recoil speed (relative to Earth at rest before the collision)? b) What fraction of the meteor's kinetic energy was transformed to kinetic energy of the Earth? c) By how much did the Earth's kinetic energy change as a result of this collision? (Ch 7 - #74) a) 6.3 x 10^-13 m/s b) 2.5 x 10^-17 c) 1.2 J Astronomers estimate that a 2.0-km diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on earth. a) Assume a spherical asteroid has a mass of 3200 kg of each cubic meter of volume and moves toward the Earth at 15 km/s. How much destructive energy could be released when it embeds itself in the Earth? b) For comparison, a nuclear bomb could release about 4.0 x 10^6 J. How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth? (Ch 7 - #81) a) 1.5 x 10^21 J b) 38,000 bombs The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 4.0 s. What is the angular acceleration as the blades slow down? (Ch 8 - #4) -170 rad/s^2 A child rolls a ball on a level floor 3.5 m to another child. If the ball makes 12.0 revolutions, what is its diameter? (Ch 8 - #6) 9.3 x 10^-2 m Hint: The movement is all linear distance 2πr = πd A grinding wheel 0.35 m in diameter rotates at 2200 rpm. a) Calculate its angular velocity in rad/s. b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? (Ch 8 - #7) a) 230 rad/s b) velocity = 40 m/s acceleration = 93000 m/s^2 A 61-cm diameter wheel accelerates uniformly about its center from 120 rpm to 280 rpm in 4.0 s. Determine: a) Its angular acceleration b) The radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. (Ch 8 - #14) a) 4.2 rad/s^2 b) rad = 130 m/s^2 tan = 1.3 m/s^2 Hint: b) Must find the angular velocity at 2.0 s! At the start of traveling to the Moon, the astronauts accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft is like a cylinder with a diameter of 8.5 m. a) Determine the angular acceleration b) The radial and tangential components of the linear acceleration of a point on the skin of the ship 6.0 min after it started this acceleration. (Ch 8 - #15) a) 1.5 x 10^-4 rad/s^2 b) rad = 1.2 x 10^-2 m/s^2 tan = 6.2 x 10^-4 m/s^2 Hint: b) The angular speed is different after 6.0 minute. An automobile engine slows down from 3500 rpm to 1200 rpm in 2.5 s. Calculate: a) Its angular acceleration b) The total number of revolutions the engine makes in this time (Ch 8 - #17) a) -96 rad/s^2 b) 98 rev Hint: b) use constant acceleration equation Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge", which takes 1.0 min to turn through 23 complete revolutions before reaching its final speed. a) What was its angular acceleration? b) What was its final angular speed in rpm? (Ch 8 - #19) a) 46 rev/min^2 b) 46 rpm The tires of a car make 75 revolutions as the car reduces its speed uniformly from 95 km/h to 55 km/h. The tires have a diameter of 0.80 m. a) What was the angular acceleration of the tires? b) If the car continues to decelerate at this rate, how much more time is required for it to stop? c) How far does it go? (Ch 8 - #22) a) -3.1 rad/s^2 b) 12 seconds c) 95 m Hint: b) the angular acceleration must be multiplied by the radius c) given velocity and must be changed into angular velocity!! keep on converting from angular to normal, back to angular Calculate the net torque about the axle of the wheel shown in the figure. Assume that a friction torque of 0.60 m N opposes the motion. Circle with radius of 12 cm and angle of 135 degrees. 1) 35 N coming off of radius 2) 28 N coming off of diameter 24 cm 3) 18 N coming off of diameter 24 cm (Ch 8 - #25) 1.2 m N clockwise Hint: Torque applied = rT - rT - rT Net torque = rT - rT - rT + friction A person exerts a horizontal force of 42 N on the end of a door 96 cm wide. What is the magnitude of the torque if the force is exerted a) Perpendicular to the door? b) At a 60.0 degree angle to the face of the door? (Ch 8 - #26) a) 40 m N b) 35 m N Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim and tire have a combined mass of 1.1 kg. (Ch 8 - #31) 0.12 kg m^2 A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg. Calculate a) Its moment of inertia about its center b) The applied torque needed to accelerate it from rest to 1750 rpm in 5.00 s. Take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 55.0 s. (Ch 8 - #34) a) 1.37 x 10^-3 kg m^s b) 5.42 x 10^-2 m N Hint: Frictional torque is negative! So when you subtract it from the other side, it is really an addition A helicopter rotor blade has three long thing rods. a) If each of the three rotor blades is 3.75 m long and has a mass of 135 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation. b) How much torque must the motor apply to bring the blades from rest up to a speed of 6.0 rev/s in 8.0 s? (Ch 8 - #43) a) 1900 kg m^2 b) 8900 m N Hint: I (thin rod) = 1/3mr^2 A centrifuge rotor rotating at 9200 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.20 m N. If the mass of the rotor is 3.10 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest, and how long will it take? (Ch 8 - #44) 480 revolutions 6.3 seconds Hint: which part of the equation are you missing? what alternative form can you use to solve for acceleration? To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets. Suppose that the satellite has a mass of 3600 kg and a radius of 4.0 m, and that the rockets each add a mass of 250 kg. What is the steady force required of each rocket if the satellite is to reach 32 rpm in 5.0 min, starting from rest? (Ch 8 - #45) 31 N Hint: Torque net = Fr Moment of Inertia = 1/2mr^2 + 4mr^2 (one cylinder and four normal blasters) T = Ia FR = Ia A bowling ball of mass 7.25 kg and radius of 10.8 cm rolls without slipping down a lane at 3.10 m/s. Calculate its total kinetic energy. (Ch 8 - #52) 48.8 J Hint: KE = KEcm + KErotational (substitute Icm for 2/5mr^2 and W for v/r) A merry-go-round has a mass of 1440 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00 s? (Ch 8 - #55) 1.63 x 10^4 J Hint: Assume it is a solid cylinder. Work is the net kinetic energy for rotation. A sphere of radius 34.5 cm and mass 1.80 kg starts from rest and rolls without slipping down a 30.0 degree incline that is 10.0 m long. a) Calculate its translational and rotational speeds when it reaches the bottom. b) What is the ratio of translational to rotational KE at the bottom? c) Do your answers in a or b depend on the radius of the sphere or its mass? (Ch 8 - #56) a) v = 8.37 m/s; w = 24.3 rad/s b) 5/2 c) Only the angular speed depends on the radius Hint: a) v = square root (10/7)gh A diver can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed (rev/s) when in the straight position? (Ch 8 - #64) 0.38 rev/s Hint: Angular momentum! a) What is the angular momentum of a figure skater spinning at 3.0 rev/s with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 48 kg? b) How much torque is required to slow her to a stop in 4.0 s, assuming she does not move her arms? (Ch 8 - #66) a) 10 kg m^2/s b) -2.5 m N A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 820 kg m^2. The platform rotates without friction with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform. a) Calculate the angular velocity when the person reaches the edge. b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk. (Ch 8 - #67) a) 0.52 rad/s b) KE initial = 370 J KE final = 200 J Hint: a) conservation of momentum; the ending moment of inertia will include both the platform and the person A uniform disk turns at 3.3 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk. They then turn together around the axis with their centers superposed. What is the angular frequency in rev/s of the combination? (Ch 8 - #72) 2.0 rev/s Hint: Watch the moment of inertia formula used Suppose a 65-kg person stands at the edge of a 5.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1850 kg m^2. The turntable is at rest initially, but when the person begins running at a speed of 4.0 m/s around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable. (Ch 8 - #74) -0.31 rad/s Hint: Use Wperson = V + Vtable/R; Vtable= WtableR A cyclist accelerates from rest at a rate of 1.00 m/s^2. How fast will a point at the top of the rim of the tire (diameter 68.0 cm) be moving after 2.25 s? (Ch 8 - #79) 4.50 m/s Hint: 2(Vo + at) = V A particular tower crane is about to lift a 2800-kg air-conditioning unit. The crane's dimensions are 3.4 m to the left of the middle vertical axis and 7.7 m to the right. a) Where must the crane's 9500-kg counterweight be placed when the load is lifted from the ground? b) Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent. (Ch 9 - #3) a) 2.3 m b) 4200 kg Hint: a) Draw diagram with all forces working. Which equilibrium condition relates distance and mass? Two cords support a chandelier and the upper cord makes a 45 degree angle with the ceiling. If the cords can sustain a force of 1660 N without breaking, what is the maximum chandelier weight that can be supported? (Ch 9 - #7) 1200 N Hint: One cord is attached to the ceiling and one is attached horizontally to the wall on the right side. Two tress are 6.6 m apart. A backpacker is trying to lift his pack out of the reach of bears. Calculate the magnitude of the force that he must exert downward to hold a 19-kg backpack so that the rope sags at its midpoint by a) 1.5 m b) 0.15 m (Ch 9 - #8) a) 225 N (round up to 230 N) b) 2050 N (round up to 2100 N) Hint: Diagram is similar to the tightrope problems. A 75-kg adult sits at one end of a 9.0-m long board. His 25-kg child sits on the other end. a) Where should the pivot be placed so that the board is balanced? b) Find the pivot point if the board is uniform and has a mass of 15 kg. (Ch 9 - #11) a) 2.3 m from the adult b) 2.5 m from the adult Hint: a) cancel out the effects of gravity and then calculate final answer b) include all forces to calculate torque; the distance of the pivot is (L /2 - X) Find the tension in the two wires supporting the traffic light. The left wire makes a 53 degree angle and the right makes a 37 degree angle. The traffic light has a mass of 33 kg. (Ch 9 - #13) Fa (53) = 260 N Fb (37) = 190 N Hint: Use substitution! Calculate the Fa and Fb for the beam. The downward forces represent the weights of the machinery on the beam. Assume the beam is uniform and has a mass of 280 kg. Fa up, 4300 N down, 3100 N down, 2200 N down, Fb up 2.0 m, 4.0 m, 3.0 m, 1.0 m (Ch 9 - #16) Fa = 6300 N Fb = 6100 N Hint: Do not forget to add the force of the beam itself into the calculations! Use substitution! A shop sign weighting 215 N hangs from the end of a uniform 155-N beam. Find the tension in the supporting wire (at 35 degree) and the horizontal and vertical forces exerted by the hinge on the beam at the wall. The distance from the hinge to the wire is 1.35 m and from the hinge to the end of the beam is 1.70 m. (Ch 9 - #18) Fw = 642 N Fh (horizontal) = 526 N Fh (vertical) = 2 N Hint: There are four total forces acting on the system. Watch the lengths or distances of the forces present. A 20.0 m long uniform beam weighting 650 N rests on walls A and B. a) Find the maximum weight of a person who can walk to the extreme end D without tipping the beam. b) Find the forces that the walls A and B exert on the beam when the person is standing at D c) Find the forces that the walls A and B exert on the beam when the person is standing 2.0 m to the right of A. Diagram: C A B D 3.0 m, 12.0 m, B- D not stated (Ch 9 - #22) a) 650 N b)Fa= 0, Fb= 1300 N c) Fa = 810 N, Fb = 490 N Hint: a) Set Fa = 0 because this is an extreme case of tripping and at this point, no support would be exerted on this part of the beam. Use Fb as the fulcrum. c) Diagram changes. Use Fb as fulcrum again. A 0.75-kg sheet is centered on a clothesline. The clothesline on either side of the hanging sheet makes an angle of 3.5 degree with the horizontal. Calculate the tension in the clothesline on either side of the sheet. Why is the tension so much greater than the weight of the sheet? (Ch 9 - #23) 60 N A 172-cm tall person lies on a light (massless) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet. The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the bottom of her feet? (Ch 9 - #24) 0.0905 m Hint: Use the center of mass as the axis. Be aware that you can cancel out the presence of the g's. a) Calculate the magnitude of the force, Fm, required of the deltoid muscle to hold up the outstretched arm. The total mass of the arm is 3.3 kg. b) Calculate the magnitude of the force, Fj, exerted by the shoulder joint on the upper arm and the angle (to the horizontal) at which it acts. Fj points down, Fm points up at 15 degree angle (12 cm), mg down (24 cm) (Ch 9 - #34) a) Fm = 250 N b) Fj = 240 N Hint: a) Make sure the force you are solving for is perpendicular to the axis!!! b) Make sure you consider both the vertical and horizontal components when solving for the resultant of Fj. The Leaning Tower of Pisa is 55 m tall and about 7.7 m in radius. The top is 4.5 m of center. is the tower in stable equilibrium? If so, how much farther can it lean before it becomes unstable? (Ch 9 - #38) Yes, because 7.7-4.5 = 3.2 which means it is still within the dimensions of the original base. It can lean 10.9 m more before becoming unstable. Hint: 2 x base = how far it can lean before becoming unstable; be sure to subtract the distance already shifted from the original position A marble column of cross-sectional area 1.4 m^2 supports a mass of 25,000 kg. a) What is the stress within the column? b) What is the strain? (Ch 9 - #41) a) 175000 N/m^2 b) 3.5 x 10^-6 Hint: E (marble) = 50 x 10^9 A sign (mass 1700 kg) hangs from the bottom end of a vertical steel girder with a cross-sectional area of 0.012 m^2. a) What is the stress within the girder? b) What is the strain on the girder? c) If the girder is 9.50 m long, how much is it lengthened? (Ch 9 - #43) a) 1.4 x 10^6 N/m^2 b) 6.9 x 10^-6 c) 6.6 x 10^-5 m Hint: E = 200 x 10^9 N/m^2 One liter of alcohol (1000 cm^3) in a flexible container is carried to the bottom of the sea, where the pressure is 2.6 x 10^6 N/m^2. What will be its volume there? (Ch 9 - #44) 997.5 cm^3 Hint: ΔV = -ΔVoΔP/B (be sure to find the change in pressure compared to atmospheric pressure) V = Vo + ΔV B = 1.0 x 10^9 a) What is the minimum cross-sectional area required of a vertical steel cable from which is suspended a 270-kg chandelier? Assume a safety factor of 7.0. b) If the cable is 7.5 m long, how much does it elongate? (Ch 9 - #53) a) 3.7 x 10^-5 m^2 b) 2.7 x 10^-3 m Hint: a) tensile strength = F/A (be sure to multiple by safety factor) Assume the supports of the uniform cantilever (m= 2900 kg) are made of wood. Calculate the minimum cross-sectional area required of each, assuming a safety factor of 9.0. Fa (20.0 m), Fb, center of gravity (distance from Fb to end is 30.0 m) (Ch 9 - #54) Aa = 1.6 x 10^-3 m^2 Ab = 9.1 x 10^-3 m^2 Hint: Find the forces for each using torque. Be aware of the signs of your answers! (+) = tensile, (-) = compressive The center of gravity of a loaded truck depends on how the truck is packed. If it is 4.0 m high and 2.4 m wide, and its CG is 2.2 m above the ground, how steep a slope can the truck be parked on without tipping over? (Ch 9 - #62) 29 degrees Hint: Angle at the center of gravity pointing downward is the same as the angle of the slope. Use tan. When a mass of 25 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12 degree with the horizontal. Determine the radius of the wire. (Ch 9 - #65) 3.5 x 10^4 m Hint: Area = πr ^2; E (aluminum) = 70 x 10^9 N/m^2 Lengths of half the wire: horizontal = L/2; vertical = L + ΔL/2 (1/cosdelta - 1) A tightly stretched horizontal "high wire" is 36 m long. It sags vertically 2.1 m when a 60.0-kg tightrope walker stands at its center. What is the tension in the wire? Is it possible to increase the tension in the wire so that there is no sag? (Ch 9 - #75) Ft = 2500 N It is not possible to increase the tension so there is no sag because a vertical force must be exerted to balance the force of gravity. A door 2.30 m high and 1.30 m wide has a mass of 13.0 kg. A hinge 0.40 m from the top and anther hinge 0.40 m from the bottom each support half the door's weight. Determine the horizontal and vertical force components exerted by each hinge on the door. (Ch 9 - #29) Fax = 55.2 N Fay = 63.7 N Fbx = 55.2 N Fby = 63.7 N Hint: Fay = Fby = 1/2mg (each hinge holds half of the door's weight) Torque (using Fb as axis) = mg(w/2) = Fax(h-2d) If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 54 cm x 31 cm x 22 cm, what would its mass be? (Ch 10 - #3) 710 kg Hint: Density of gold = 19.3 x 10^3 Estimate the pressure exerted on a floor by: a) One pointed heel of area 0.45 cm^2 b) One wide heel of area 16 cm^2. The person wearing the shoes has a mass of 56 kg. (Ch 10 - #9) a) 6.1 x 10^6 N/m^2 b)1.7 x 10^5 N/m^2 Hint: Calculating for one heel only!!! And watch the conversion between cm^2 and m^2. a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. b) What will be the pressure against the side of the pool near the bottom? (Ch 10 - #16) a) P = 1.19 x 10^5 N/m^2 F = 2.8 x 10^7 N b) The same as the pressure from part a! Both at the bottom of the pool. Hint: Density of water = 1.00 x 10^3 kg/m^3 Pressure of atm = 1.013 x 10^5 N/m^2 Area = length x width (NOT DEPTH) A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61 degree from the horizontal. a) Determine the water gauge pressure at the house. b) How high could the water shoot if it came vertically out of a broken pipe in the front of the house? (Ch 10 - #17) a) 7.0 x 10^5 N/m^2 b) 72 m Hint: a) Don't forget to add the water tower as part of the height! Water and then oil are poured into a U-shaped tube, open at both ends. They come to equilibrium. What is the density of the oil? Oil takes up 27.2 cm, water has 8.62 cm on top that is empty. (Ch 10 - #18) 683 kg/m^3 Hint: Pressure at point A and B are the same because the fluids are at the same height and in the same liquid! If it was not.. the stuff would be moving! A hydraulic press for compacting powdered samples has a large cylinder which is 10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm. A lever is attached to the small cylinder. There sample, which is placed on the large cylinder, has an area of 4.0 cm^2. What is the pressure of the sample if 320 N is applied to the lever? (Ch 10 - #21) 4.0 x 10^7 N/m^2 Hint: There are four forces acting on the system! Find the torque. Substitute into P1=P2 (area = piR^2) *Remember that Fb = Fsample because it moves into the other* Plug into pressure equation What fraction of a piece of iron will be submerged when it floats in mercury? (Ch 10 - #23) 57% Hint: Density of iron = 7.8 x 10^3 kg/m^3 Density of mercury = 13.6 x 10^3 kg/m^3 What is the likely identity of a metal if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water? (Ch 10 - #27) 7840 kg/m^3 (iron or steel) Hint: Apparent Weight = Actual Weight - F(buoyancy) m(apparent)g = m(metal)g - density(g)(V) V = volume of water = mass(metal)/density(metal) Solving for density of metal! The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water? (Ch 10 - #31) 0.105 or 10.5% Hint: Simplify the formula for F(buoyancy of seawater) = Weight(ice) Vabove = Vice - Vsubmerged A 0.48-kg piece of wood floats in water but is found to sink in alcohol (SG=0.79), in which it has an apparent mass of 0.047 kg. What is the SG of the wood? (Ch 10 - #35) 0.88 A 5/8-in diameter garden hose is used to fill a round swimming pool 6.0 m in diameter. How long will it take to fill the pool to a depth of 1.4 m if water flows from the hose at a speed of 0.40 m/s? (Ch 10 - #48) 6 days Hint: Be sure to convert the units of inches to m! (39.37 in = 1 m) Volume = (pi)(r^2)(depth) Area = 1/2(pi)(r^2) A 180-km/h wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is 6.2 m x 12.4 m in size, estimate the weight of the roof. Assume the roof is not nailed down. (Ch 10 - #49) 1.2 x 10^5 N Hint: Weight indicates finding the force!!!!! We assume that the height of the two sides of the roof are the same Weight of the roof = mg = Force Density (air) = 1.29 kg/m^3 What is the lift on a wing of area 88 m^2 if the air passes over the top and bottom surfaces at speeds of 280 m/s and 150 m/s, respectively? (Ch 10 - #52) 3.2 x 10^6 N Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above, where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. (Ch 10 - #53) Flow velocity = 2.5 m/s Gauge Pressure = 2.2 atm Hint: For gauge pressure, use Bernoulli's Equation and substitute in the absolute pressure equation Must convert atm to Pa and vice versa at the end and the beginning!!!!! (1 atm = 1.013 x 10^5 Pa) A gardener feels it is taking too long to water a garden with a 3/8-in diameter hose. By what factor will the time be cut using a 5/8-in diameter hose instead? (Ch 10 - #60) Time has been cut by 87% Hint: t1(R1^4) = t2(R2^4) Assuming a constant pressure gradient, if blood flow is reduced by 65%, by what factor is the radius of a blood vessel decreased? (Ch 10 - #64) The vessel has been decreased by 23% Hint: Reduced by 65% leaves only 36% working. Intravenous transfusions are often made under gravity. Assuming the fluid has a density of 1.00 g/cm^3, at what height should the bottle be placed so the liquid pressure is: a) 52-mmHg b) 680 m-H2O c) If the blood pressure is 75-mmHg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein? (Ch 10 - #74) a) 0.71 m b) 0.68 m c) 1.0 m Hint: Must convert to get only meters as the answer!!!! 1-mmHg = (133 N/m^2) 1 mH20 = (9.80 N/m^2) Or memorize that 1.00 g/cm^3 = 1,000 kg/m Estimate the difference in air pressure between the top and the bottom of the Empire State Building in NYC. It is 380 m tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level. (Ch 10 - #76) ΔP = 0.047 atm Hint: Use ΔP = density(g)(Δh) and then divide by pressure at sea level to get a fraction answer A simple model considers a continent as a block (density = 2800 kg/m^3) floating in the mantle rock around it (density = 3300 kg/m^3). Assuming the continent is 35 km thick, estimate the height of the continent above the surrounding mantle rock. (Ch 10 - #84) 5.3 km Hint: Y = [1-(density of continent/density of mantle)] x height A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Assume the specific gravity of the wood is 0.60. (Ch 10 - #86) 72.97 = 72 people can fit on the raft before they start getting wet Hint: Weight of water displaced = Weight of people + weight of logs (only dealing with weight here... not looking at the pressure of force exerted by the people and logs) Volume (log) = (pi)(r^2)(length) During each heartbeat, approximately 70 cm^3 of blood is pushed from the heart at an average pressure of 105-mmHg. Calculate the power output of the heart, in watts, assuming 70 beats per minute. (Ch 10 - #88) 1.14 W Hint: Power = work/time or PV/t