The following Activities are for the 'Friction and Internal Energy' applet. Make sure you know how the applet functions by consulting Help and ShowMe under Applet Help on the applet's Help menu.

Activity 1. The purpose of Activity 1 is to investigate what happens to the work done on the block by the applied force when the block is moving with constant speed and its kinetic energy is not changing.

Exercise 1. RESET the applet. Set the following parameters and the following initial conditions at t = 0 for the block:

• mass: m = 5.0 kg
• initial position: x(0) = 0
• initial velocity: v_x(0) = 2.0 m/s
• magnitude of applied force: F_appl = 9.8 N
• direction of applied force: q = 0^o
• kinetic coefficient of friction: m_k = 0.20

Display the energy box. With the settings above, it displays two columns of non-zero height, the kinetic energies KE(0) and KE. Of course, at t = 0 the instantaneous kinetic energy KE is necessarily equal to the initial kinetic energy KE(0). At the start, the work W_appl done by the applied force and the change DU in the internal energy of the block-table system are zero.

Exercise 2. PLAY the motion, and observe the changes in the energy bars. PAUSE the applet. Then REWIND it, and observe again. In a sentence or two, write down what you observe and explain the change in the internal energy U of the block-table system in view of energy conservation.

Exercise 3. Display the data box when the motion is paused, and given the values of t, v_x, and F_appl, calculate the change Dx in the block's position and the work done on the block by the applied force. From the latter, given that the block's kinetic energy is constant in this case, predict the change DU in the internal energy of the block-table system. Compare your answers to the values in the data box.

Question. Why is the work W_appl done by the applied force on the block equal to the change in internal energy of the block-table system, and not equal to the change in internal energy of just the block?

Answer. W_appl is the total external work done on the block-table system and, by the law of energy conservation, must equal the change in the total energy of this system. The system's energy consists of two parts: kinetic energy and internal energy. The kinetic energy is constant in this case. Therefore, W_appl must be equal to the change in the internal energy of this system.

It is possible theoretically to consider just the block alone. However, then must add to W_appl the work W_fric done by the friction force acting on the block. The sum is the total external work done on the block and, by energy conservation, must equal the change in the block's energy. However, in practice, it is impossible to calculate W_fric. To calculate this work one would need to know the tiny displacements of the surface irregularities at the bottom of the block during the block's motion and the individual forces acting on these.

Note that W_fric is not equal to -W_appl. If that were the case, the block's internal energy would have to remain constant, which is clearly not true. The block gets warmer which means that its internal energy must increase.

Activity 2. The purpose of this Activity is to investigate what happens to the work done on the block by the friction force when there is no applied force acting on the block.

Exercise 1. RESET the applet. Set the following parameters and the following initial conditions at t = 0 for the block:

• mass: m = 5.0 kg
• initial position: x(0) = 0
• initial velocity: v_x(0) = 2.0 m/s
• magnitude of applied force: F_appl = 0
• direction of applied force: q = 0^o
• kinetic coefficient of friction: m_k = 0.20

Display the energy box. With the settings above, it displays two columns of non-zero height, the kinetic energies KE(0) and KE. Of course, at t = 0 the instantaneous kinetic energy KE is necessarily equal to the initial kinetic energy KE(0). At the start, the work W_appl done by the applied force and the change DU in the internal energy of the block-table system are zero.

Exercise 2. PLAY the motion, and observe the changes in the energy bars until the block comes to a stop. Then REWIND the applet, and observe again. In a sentence or two, write down what you observe and explain the change in the internal energy U of the block-table system in view of energy conservation.

Exercise 3. From the settings of m and v_x(0), calculate the value KE(0) of the initial kinetic energy, and predict the change in the internal energy of the block-table system from the beginning of the motion until the motion comes to a stop. Compare your results with the values listed in the data box.

Exercise 4. REWIND the applet, display the data box, and note down the value of the friction force. Calculate this value from the settings for m and m_k.

PLAY the motion until the block comes to a stop. Given the values of t, v_x(0), F_fric,x (during the motion, F_fric,x is unequal to 0), and m, calculate the block's displacement Dx until the block comes to a stop.

Calculate the product F_fric,xDx. This product looks like it is equal to the work W_fric done by friction. However, it is not equal to W_fric because Dx is not equal to the displacements of the small irregularites at the bottom of the block that momentarily lock with those at the surface of the table, bend, and brake contact while the block is moving. We need to consider these latter displacments to calculate W_fric.

F_fric,xDx = DK + DU_block (INCORRECT).

Since W_appl = 0 in the present case, this equation should give us the change in the block's internal energy if F_fric,xDx were indeed the friction work W_fric. You should find F_fric,xDx = -10.0 J. Together with DK = -10.0 J, the preceding equation, if true, would imply DU_block = 0. This is clearly incorrect because DU_block is greater than zero. The block's internal energy increases as the block is sliding to a stop while getting warmer.

The moral of this story is that we cannot calculate friction work by using the displacement of the center of mass of the block and that there is no practical way of calculating the change in the block's internal energy resulting from the presence of friction. We only can calculate the change in the internal energy of the block-table system for which we do not need to calculate the work done by friction because this work does not amount to an external transfer of energy for the block-table system.

Activity 3. The purpose of this Activity is repeat the kinds of observations and calculations from Activities 1 and 2 in a more general case where the velocity is not constant and the motion does not come to a stop.

Exercise 1. RESET the applet. Set the following parameters and the following initial conditions at t = 0 for the block:

• mass: m = 5.0 kg
• initial position: x(0) = 0
• initial velocity: v_x(0) = -2.0 m/s
• magnitude of applied force: F_appl = 20.0 N
• direction of applied force: q = 0^o
• kinetic coefficient of friction: m_k = 0.20

Make observations and calculations like those in Activities 1 and 2, and write down what you observe and conclude.

Exercise 2. Repeat Exercise 1, but with an applied force that is not horizontal. E.g., take q = 30^o.