Physics 111A - Lab Report
Lab 109: One-Dimensional Motion at Constant Acceleration
Introduction
The objective of this experiment is to observe the one dimensional motion of a cart with constant
acceleration and changing masses in order to see how motion is related to the three kinematic
equations; graphically represented by the raw data we gathered while testing the carts velocity at
three different angles.
Theoretical Background
One-dimensional motion is when a particle is constrained to move along a straight line. When we
say that we want to describe the particle's motion, we mean that we want to be able to say where
it is at what time. We want to know the particle's position as a function of time, which we will
label as 𝑥(𝑡). The function will only be meaningful if:
- we specify an x-axis and the direction that corresponds to increasing values of 𝑥
- we specify an origin where 𝑥=0
- we specify the units for the quantity, 𝑥.
The distance is considered the total length traveled by the moving object. It is a scalar quantity
and does not consider the direction. The velocity of the cart is the rate of change an object’s
position is with respect to time. Velocity has both magnitude and direction, defined as:
Acceleration refers to when an object's velocity changes. Average acceleration is defined as the
change in velocity divided by the time taken for that change:
Since gravity is proportional to mass, the acceleration of an object doesn’t depend on its own
mass. E.g, a bowling ball has the same acceleration as a feather given they are in a vacuum
sealed room with no air resistance.
Procedure
The Equipment used in our experiment consists of
- Data collection system(computer and PASCO Capstone software)
, - Dynamics Track
- Wireless Smart Cart
- Dynamics Track End Stop
- Dynamics Track Rod Clamp
- Tripod Stand
- Cart Mass(x2)
- Digital Protractor
- Ruler
Set up
Adjust the track to the specified angle of interest(3, 6, and 9 degrees) and line the cart to the end
of the inclined plane. Press the record button on the software and release the cart. Press stop
recording right before the cart makes contact with the end stopper. The software will record two
graphs. One is a position-time graph, and the other is a velocity-time graph. Using the quadratic
formula ax^2 + bx + c = 0, we know that the derivative of the displacement function is velocity
with respect to time. In this case, that is 2ax. The derivative of velocity is acceleration,
represented by the tangent line on our graph. In part 2 of our experiment, we needed the inclined
plane to be an angle that gave us a constant acceleration of 1m/s^2. Since the equation for
acceleration was a = sin (theta), we took the inverse sine of 1/-9.8 to find the angle. We then
repeated the experiment with both 250g and 500g of weight on the cart to figure out how mass
affects the cart's acceleration down the slope.
Results & Calculations
C Inclined Theoretical Acceleration Acceler Acceleratio Acceler
a Angle, Acceleration, a = ation n ation
s θ[degree] gsinθ
e
Set Actual a_exp1 from % error A_exp2 % error
value value position vs. from
time curve velocity vs.
time curve
1 3 2.83 0.484 (0.235*2)=0.47 2.89% 0.471 2.66%
2 6 6.07 1.036 (0.53*2)=1.06 2.32% 1.06 2.32%
3 9 8.97 1.527 (.788*2)=1.576 3.2% 1.57 2.82%
Theoretical Calculations
Theoretical Calculation for the Acceleration:
Lab 109: One-Dimensional Motion at Constant Acceleration
Introduction
The objective of this experiment is to observe the one dimensional motion of a cart with constant
acceleration and changing masses in order to see how motion is related to the three kinematic
equations; graphically represented by the raw data we gathered while testing the carts velocity at
three different angles.
Theoretical Background
One-dimensional motion is when a particle is constrained to move along a straight line. When we
say that we want to describe the particle's motion, we mean that we want to be able to say where
it is at what time. We want to know the particle's position as a function of time, which we will
label as 𝑥(𝑡). The function will only be meaningful if:
- we specify an x-axis and the direction that corresponds to increasing values of 𝑥
- we specify an origin where 𝑥=0
- we specify the units for the quantity, 𝑥.
The distance is considered the total length traveled by the moving object. It is a scalar quantity
and does not consider the direction. The velocity of the cart is the rate of change an object’s
position is with respect to time. Velocity has both magnitude and direction, defined as:
Acceleration refers to when an object's velocity changes. Average acceleration is defined as the
change in velocity divided by the time taken for that change:
Since gravity is proportional to mass, the acceleration of an object doesn’t depend on its own
mass. E.g, a bowling ball has the same acceleration as a feather given they are in a vacuum
sealed room with no air resistance.
Procedure
The Equipment used in our experiment consists of
- Data collection system(computer and PASCO Capstone software)
, - Dynamics Track
- Wireless Smart Cart
- Dynamics Track End Stop
- Dynamics Track Rod Clamp
- Tripod Stand
- Cart Mass(x2)
- Digital Protractor
- Ruler
Set up
Adjust the track to the specified angle of interest(3, 6, and 9 degrees) and line the cart to the end
of the inclined plane. Press the record button on the software and release the cart. Press stop
recording right before the cart makes contact with the end stopper. The software will record two
graphs. One is a position-time graph, and the other is a velocity-time graph. Using the quadratic
formula ax^2 + bx + c = 0, we know that the derivative of the displacement function is velocity
with respect to time. In this case, that is 2ax. The derivative of velocity is acceleration,
represented by the tangent line on our graph. In part 2 of our experiment, we needed the inclined
plane to be an angle that gave us a constant acceleration of 1m/s^2. Since the equation for
acceleration was a = sin (theta), we took the inverse sine of 1/-9.8 to find the angle. We then
repeated the experiment with both 250g and 500g of weight on the cart to figure out how mass
affects the cart's acceleration down the slope.
Results & Calculations
C Inclined Theoretical Acceleration Acceler Acceleratio Acceler
a Angle, Acceleration, a = ation n ation
s θ[degree] gsinθ
e
Set Actual a_exp1 from % error A_exp2 % error
value value position vs. from
time curve velocity vs.
time curve
1 3 2.83 0.484 (0.235*2)=0.47 2.89% 0.471 2.66%
2 6 6.07 1.036 (0.53*2)=1.06 2.32% 1.06 2.32%
3 9 8.97 1.527 (.788*2)=1.576 3.2% 1.57 2.82%
Theoretical Calculations
Theoretical Calculation for the Acceleration:
