Work Power and Efficiency
.A person pushes a 10.0 kg mass at constant speedacross μ = 0.150, 8.50 m long floor
1
at constant speed.
a) How much work does the person do?
b) How much work does friction do?
Ans:
For part A, since the person is pushing the mass with aconstant velocity, which means
no acceleration, forces are balanced, and applied force is equal to friction force.
Givens:
→ →
𝐹𝑎𝑝 = 𝐹𝑓𝑟
→ →
𝐹𝑎𝑝 = μ𝐹𝑁
→ →
𝐹𝑎𝑝 = μ𝑚𝑔
→ 𝑁
𝐹𝑎𝑝 = 0. 150(10. 0𝑘𝑔)(9. 8 𝑘𝑔 )
→
𝐹𝑎𝑝 = 14. 7𝑁
→→
Now, we have the applied force. To calculate the work, use the equation𝑊 = 𝐹𝑑
.
→→
= 𝐹𝑑
𝑊
𝑊 = 14. 7𝑁(8. 50𝑚)
𝑊 = 125𝑁𝑚 (s ince𝑊 = Δ𝐸, which means the unit𝑁𝑚is equal to𝐽)
𝑊 = 125𝐽
For part B, since the applied force is equal to friction force because of constant velocity,
the work done by friction is also equal to125𝐽but negative, so the answer is− 125𝐽.
.Find the power required for a crane to lift a400. 0𝑘𝑔mass at constant speed100. 0
2
meters in30. 0seconds. If the crane consumes35𝑘𝑊of electrical power, find its
efficiency.
Ans:
𝑤
To find the power, use the equation𝑃 = 𝑡
. Since the crane lifts the mass atconstant
s peed, which means there is no acceleration. The appliedforce is equal to the gravity
force.
Givens:
𝑤
𝑃 = 𝑡
.A person pushes a 10.0 kg mass at constant speedacross μ = 0.150, 8.50 m long floor
1
at constant speed.
a) How much work does the person do?
b) How much work does friction do?
Ans:
For part A, since the person is pushing the mass with aconstant velocity, which means
no acceleration, forces are balanced, and applied force is equal to friction force.
Givens:
→ →
𝐹𝑎𝑝 = 𝐹𝑓𝑟
→ →
𝐹𝑎𝑝 = μ𝐹𝑁
→ →
𝐹𝑎𝑝 = μ𝑚𝑔
→ 𝑁
𝐹𝑎𝑝 = 0. 150(10. 0𝑘𝑔)(9. 8 𝑘𝑔 )
→
𝐹𝑎𝑝 = 14. 7𝑁
→→
Now, we have the applied force. To calculate the work, use the equation𝑊 = 𝐹𝑑
.
→→
= 𝐹𝑑
𝑊
𝑊 = 14. 7𝑁(8. 50𝑚)
𝑊 = 125𝑁𝑚 (s ince𝑊 = Δ𝐸, which means the unit𝑁𝑚is equal to𝐽)
𝑊 = 125𝐽
For part B, since the applied force is equal to friction force because of constant velocity,
the work done by friction is also equal to125𝐽but negative, so the answer is− 125𝐽.
.Find the power required for a crane to lift a400. 0𝑘𝑔mass at constant speed100. 0
2
meters in30. 0seconds. If the crane consumes35𝑘𝑊of electrical power, find its
efficiency.
Ans:
𝑤
To find the power, use the equation𝑃 = 𝑡
. Since the crane lifts the mass atconstant
s peed, which means there is no acceleration. The appliedforce is equal to the gravity
force.
Givens:
𝑤
𝑃 = 𝑡
