Block sliding down frictionless ramp while being pulled with constant force?

In summary, the conversation is about a block of ice sliding down a frictionless ramp at an angle of 60 degrees while a worker pulls on it with a constant force of 50.0 N. The kinetic energy of the block increases by 128 J over a distance of 0.8m. The task is to calculate the work done by the gravitational force and the normal force, as well as the percent increase in kinetic energy if the block slid down the ramp without the rope attached. The conversation also discusses the concept of free body diagrams and the use of formulas for work. The conclusion is that the mass of the block is not needed to solve the problem and the net work done by all forces equals the change in kinetic energy.
  • #1
soliel021
4
0

Homework Statement


A block of ice slides down a frictionless ramp at theta = 60 degrees while an ice worker pulls on the block (via a rope) with a constant force of 50.0 N. The block slides a distance d = 0.8m along the ramp and its kinetic energy increases by 128 J.
(a) Calculate the work done on the block by the gravitational force.
(b) Calculate the work done on the block by the normal force.
(c) Calculate the percent increase in its kinetic energy if it slid down the ramp the same distance with no rope attached.


Homework Equations


I have no idea, that's my problem!


The Attempt at a Solution


I don't even know where to start!
 
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  • #2
Do you know the formulas for work and concept of free body diagram(FBD, in short) ?
 
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  • #3
no and yes...

I understand the concept of free body diagrams, but there are so many formulas that I really need help choosing which ones to use for this specific problem.
 
  • #4
OK. Draw a free body diagram.
For I and II : W = F.r
You know F from FBD for both cases and r is given to you. Use your "intelligence" to find the angle between F and r and calculate the dot product in each case.
 
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  • #5
This may be a really stupid question, but what does "r" stand for? Is it displacement?
 
  • #6
r really should be s or distance i think...
 
  • #7
If it has a constant force then that must mean that F=ma is constant, therefore its acceleration isn't changing, as this would alter the force, so how is the block of ice gaining Ek due to a change in velocity?
 
  • #8
yeah, I don't get it either! and don't I need to know the mass of the block of ice?? I'm so confused...
 
  • #9
jesus1987 said:
If it has a constant force then that must mean that F=ma is constant, therefore its acceleration isn't changing, as this would alter the force, so how is the block of ice gaining Ek due to a change in velocity?

If there is an acceleration, then velocity is changing.
 
  • #10
soliel021 said:
yeah, I don't get it either! and don't I need to know the mass of the block of ice?? I'm so confused...

you don't need the mass.

Net work done by all forces = change in kinetic energy.

There are 3 forces to consider here. Gravity, the normal force, and the 50N force.

What is the work done by the normal force?

What is the work done by the 50N force?

[tex]W_{gravity} + W_{normal} + W_{50} = 128[/tex]

you can solve for Wgravity using this equation. so the idea is to solve part b) before part a).
 

1. What is the acceleration of the block down the ramp?

The acceleration of the block down the ramp would be equal to the component of the pulling force parallel to the ramp, divided by the mass of the block. This can be calculated using the formula a = Fsinθ/m, where θ is the angle of the ramp and m is the mass of the block.

2. Does the force of gravity affect the block's motion down the ramp?

Yes, the force of gravity will still act on the block even though it is being pulled with a constant force. However, since the ramp is frictionless, the force of gravity will not contribute to the acceleration of the block down the ramp.

3. How does the angle of the ramp affect the block's motion?

The angle of the ramp will affect the acceleration of the block down the ramp. The steeper the ramp, the greater the acceleration of the block due to the component of the pulling force parallel to the ramp being larger. This can be seen in the formula a = Fsinθ/m, where θ is the angle of the ramp.

4. Will the block ever reach a constant velocity down the ramp?

Assuming the pulling force remains constant, the block will continue to accelerate down the ramp. However, if the pulling force is eventually equal to the force of gravity acting on the block, then the block will reach a constant velocity known as terminal velocity.

5. How does the mass of the block affect its motion down the ramp?

The mass of the block will affect the acceleration of the block down the ramp. The larger the mass, the smaller the acceleration due to the larger denominator in the formula a = Fsinθ/m. However, assuming the pulling force remains constant, the block will still reach a constant velocity down the ramp regardless of its mass.

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