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Chapter 1: Q3DQ (page 1)

An object is released from rest at the top of a ramp. If the ramp is frictionless, does the object鈥檚 speed at the bottom of the ramp depend on the shape of the ramp or just on its height? Explain. What if the ramp is not frictionless?

Short Answer

Expert verified

If the surface is frictionless then the speed is dependent on the height of the object, and if the surface is frictional then the speed of an object depends on the shape of the ramp.

Step by step solution

01

Concept/Significance Law of Conservation of Energy

This law tells that the total energy is the sum of kinetic energy and the potential of an isolated system remains the same.

02

Determine whether the object’s speed at the bottom of the ramp depends on the shape of the ramp or just on its height, also find the same if the ramp is not frictionless

According to the conservation of energy, the total potential energy at the maximum height will be equal to the total kinetic energy at the bottom of the ramp when an object is released from rest on a frictionless surface of the ramp. In this case, there will be no loss of energy because the surface is frictionless. Therefore, the energy at the lowest point will be equal to the energy at the highest point and it will not affect the final velocity of the object in this case.

Therefore, the speed is dependent on the height of the object irrespective of the shape of the ramp.

According to the conservation of energy, when an object is released from rest from a frictional surface of the ramp, then, the total potential energy at the highest point will be dissipated to overcome the frictional losses during the path of the ramp.

Therefore, the energy at the lowest point will be less than the energy at the highest point and it will affect the final velocity of the object in this case.

Therefore, the speed of an object at the bottom of the ramp depends on the shape of the ramp.

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