Mover Pushes 700 kg Piano up 9° Ramp - Force Calculation

In summary, the net force exerted by the mover on the piano is 73 N, which is the force needed to keep the piano moving at a constant velocity on the ramp. This is because the work done by gravity gets stored as potential energy in the system and does not contribute to the net force. The force needed for the initial acceleration may be greater than 73 N, but this is not the question being asked.
  • #1
Mr Davis 97
1,462
44

Homework Statement


[/B]
A mover pushes a 700 kg piano from rest up a ramp with a 9° slope. The piano is traveling at 2 m/s when it is 3 m above the ground. How much force does the mover exert on the piano?

Homework Equations


[/B]
##W = \Delta K##

The Attempt at a Solution



I started with the equation ##F_{net}d\cos\theta = \frac{1}{2}mv^{2}##Then I solved for the net force: ##F_{net} = \displaystyle\frac{mv^{2}}{2d\cos\theta}##I then solved for displacement: ##d = \displaystyle\frac{3}{\sin9^{\circ}} = 19.2##Next, I found the net force: ##F_{net} = 73~N##This is the net force on the body, so I found the force that the mover exerted against gravity to find what he exerted, which came out to me ##1150~N##. However, this is this the incorrect answer. My textbook says that the correct answer is 73 N. But isn't this the net force on the body, and not the force that the mover exerts? Please explain what I am doing wrong.
 
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  • #2
Even though gravity also does work, this work gets stored as potential energy in the system. So the work done by gravity simply cancels out with this potential energy.
 
  • #3
paisiello2 said:
Even though gravity also does work, this work gets stored as potential energy in the system. So the work done by gravity simply cancels out with this potential energy.
I still don't understand why I am wrong. Doesn't the mover have to overcome the parallel force of gravity in addition to applying his own force to accelerate the piano?
 
  • #4
Yes, but this is stored as potential energy in the system.

PEi + KEi +Work done by mover + Work done by gravity = PEf + KEf
0 + 0 + Work done by mover + (mgsinθ)(h/sinθ) = mgh + 1/2mv2
Work done by mover = 1/2mv2
 
Last edited:
  • #5
Mr Davis 97 said:
I still don't understand why I am wrong. Doesn't the mover have to overcome the parallel force of gravity in addition to applying his own force to accelerate the piano?
For the initial acceleration more than 73N will need to be applied but that is not the question. You are only asked about the force needed when acceleration is zero.
 

Related to Mover Pushes 700 kg Piano up 9° Ramp - Force Calculation

What is the force required to push a 700 kg piano up a 9° ramp?

The force required to push the piano up the ramp can be calculated using the formula F = mg(sinθ + μcosθ), where F is the force, m is the mass of the piano, g is the acceleration due to gravity, θ is the angle of the ramp, and μ is the coefficient of friction between the piano and the ramp. Plugging in the given values, the force required to push the piano up the ramp is approximately 6,107.9 N.

How does the angle of the ramp affect the force required to push the piano?

The force required to push the piano up the ramp increases as the angle of the ramp increases. This is because the steeper the ramp, the more the weight of the piano is acting against the direction of motion, which requires a greater force to overcome.

What is the role of friction in this scenario?

Friction plays a crucial role in this scenario as it is the force that opposes the motion of the piano. As the piano moves up the ramp, the coefficient of friction between the piano and the ramp determines the amount of force required to overcome this resistance.

How can the coefficient of friction be determined?

The coefficient of friction can be determined experimentally by measuring the force required to push the piano up the ramp at different angles and using the formula μ = F/mg(cosθ - sinθ), where μ is the coefficient of friction, F is the force, m is the mass of the piano, and g is the acceleration due to gravity. It can also be estimated based on the materials of the piano and the ramp.

What are the safety considerations when pushing a heavy object up a ramp?

When pushing a heavy object up a ramp, it is important to make sure that the ramp is stable and has a non-slip surface. The person pushing the object should also wear proper footwear and use correct lifting techniques to avoid injury. It may also be necessary to use additional equipment, such as a pulley system, to reduce the force required and prevent accidents.

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