Calculating Plank's Velocity on Frictionless Ice Surface

  • Thread starter willworkforfood
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In summary, a person with a mass of 47.7 kg is standing on a plank with a mass of 77 kg on a frictionless frozen lake. The person begins to walk at a constant velocity of 2.06 m/s to the right relative to the plank. The problem is asking for the velocity of the plank relative to the ice surface. One way to solve this is by considering the problem in the moving board frame, where the initial and final momenta can be used to solve for the velocity of the plank.
  • #1
willworkforfood
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A 47.7 kg person is standing on a 77 kg plank. The plank is originally at rest on a frozen, frictionless lake. The person begins to walk along the plank at a constant velocity of 2.06 m/s to the right relative to the plank.

What is the plank's velocity relative to the ice surface in m/s?

I realize this is a momentum problem, I just don't know how to solve for the velocity of the plank with respect to the ice or of the person with respect to the ice or what a "right relative to the plank" is...

Any help is appreciated as always :smile:
 
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  • #2
Draw a diagram. If the Planck's velocity is v2 (relative to ice) into the opposite direction, what is the person's velocity (relative to ice)?
 
  • #3
One way to do this problem is to consider it in the moving board frame. That is, if the board is moving with a speed v to the left (with respect to the ice, since the person is moving to the right), then in the frame with speed v to the left you know the initial and final momenta (ie, before the person starts walking, the person and board move right (in the frame) at a speed v, and afterwards just the person is moving at the given speed) and you know momentum is conserved, so you can solve for v.
 

1. What is Plank's velocity on a frictionless ice surface?

Plank's velocity on a frictionless ice surface is the maximum speed at which an object can travel without any external forces acting upon it. This means that the velocity is constant and does not change over time.

2. How is Plank's velocity calculated on a frictionless ice surface?

Plank's velocity can be calculated using the equation v = d/t, where v is the velocity, d is the distance traveled, and t is the time taken. In the case of a frictionless ice surface, the distance traveled is the length of the ice surface and the time taken is the time it takes for the object to traverse the surface.

3. What factors affect Plank's velocity on a frictionless ice surface?

The only factor that affects Plank's velocity on a frictionless ice surface is the length of the ice surface. The longer the ice surface, the higher the velocity will be, as the object has more time to accelerate before reaching the end of the surface.

4. Can Plank's velocity be greater than the speed of light on a frictionless ice surface?

No, according to the theory of relativity, the speed of light is the maximum speed at which any object can travel. Therefore, Plank's velocity on a frictionless ice surface cannot exceed the speed of light.

5. How does friction affect Plank's velocity on a frictionless ice surface?

Friction has no effect on Plank's velocity on a frictionless ice surface, as the surface is frictionless. This means that there is no force acting against the object's motion, allowing it to maintain a constant velocity without any decrease due to friction.

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