A small block of mass m is place on top of a hill as shown in the figure at the

Question

A small block of mass m is place on top of a hill as shown in the figure at the right, a height h above a horizontal track. The hill is frictionless, but when the block reaches the horizontal track, there is a coefficient of friction, u The block slides along the track for a distance L and comes to a stop. For this motion air resistance can be ignored. We will take the origin of the coordinate system to be at A with x being the horizontal coordinate with positive to the right, and y being the vertical coordinate with positive up. We will choose our system to include the block, the hill, the surface with friction, and the Earth. The parameters of the problem are those shown in the figure: m, g, u, d1, Lr d2, h, and 6. Also, the block has a speed ve at point B at the bottom of the hill A. As the block slides from the top of the hill to point B at the bottom of the h Select energy is transformed into Select- energy. Are there any external forces that transfer energy in or out of the system as work? ---Select--- B. Use the parameters of the problem to write an expression for the known energy of the block at the top of the hill C. Use the parameters of the problem to write an expression for the known energy of the block at point B at the bottom of the hill. D. Write an expression for the speed of the block at point at the bottom of the hill energy has decreased and -Select A. When the block a at point C (where it comes to a stop) from point B at the bottom of the hill, Select Are there any external forces that transfer energy in or out of the system as work? Select-- B. Use the parameters of the problem to write an expression for the change in the form of energy that has increased from Bto C c. The change in the form of energy that increases from B to c is --Select he energy the block had at the top of the hill D. Write an expression for Lr the distance along the horizontal surface the block travels until it comes to a stop, using the other parameters of the problem energy has increased.

Explanation / Answer

1. A) As the ball slides from top of the hill to bottom of the hill potential energy is transformed into kinetic energy.

Are there any external forces that transfer energy in or out of the system as work?

We have considered the our system to inlcude the block, the hill, the surface with friction, and the earth. Any force is exterted by agent which include something from this system only. So, any external forces don't transfer energy in or out of the system.

1.B) At top of the hill the block has potential energy = mgh

1.C) applying energy conservation for the block we have:

mgh = (1/2)mvB2 = energy of the block at B.

1.D) we have mgh = (1/2)mvB2,

So, vB = 2gh = speed at bottom of the hill

2.A) When the block arrives at point C from point B, kinetic energy has decreased and heat energy has increased.

There are no external forces which transfer energy.

2.B) From B to C the whole kinetic energy has coonverted to heat energy.

So, the expression for this change in energy is =  (1/2)mvB2

2.C) The change in the form of energythat increases from B to C is mgh the energy the block had at the top of the hill.

2D) The frictional force on the block = µmg

So deceleration of the block after B = µg

So using the equation v2 - u2 = 2as we have

0 - vB2 = -2µgL (here µg is negative as it is decelration)

or L = vB2 /2µg

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification I will be happy to oblige.....

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