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

Activity 1. The purpose of Activity 1 is to determine the static coefficient of friction m_s between the block and the table.

RESET the applet. Set the static coefficient of friction to 0.30. Pretend you don't know this value and want to determine it 'experimentally' with the applet. Do so as follows.

Increase the magnitude of the force applied to the block until the block's acceleration becomes non-zero. Keep the direction of the applied force horizontal. What is the magnitude of the (static) friction force just before the block's acceleration becomes non-zero? The information is available from the data box.

Remember that the static coefficient of friction m_s determines the maximum magnitude of the static friction force via

F_fric,max = m_s N (1)

where N is the magnitude of the normal force. An equation for the magnitude of the nomal force can be obtained by applying Newton's second law in the y-direction (vertical direction) to the block. When the applied force is horizontal, only the normal force and the force of gravity acting on the block have a non-zero y-component. Since a_y = 0, Newton's seond law implies that

N - mg = 0 (2)

N = mg .(3)

Here, m is the mass of the block and g the magnitude of the acceleration due to gravity, which is taken to be equal to 9.8 m/s² in the applet.

Substitute Expression (3) for N into Eq.(1), and use the resulting equation with the given and observed values to calculate m_s. Compare your result to the value set earlier with the slider.

Activity 2. The purpose of this Activity is to determine the kinetic coefficient of friction.

Continue with the applet in the same state as in Activity 1, i.e., with m_s = 0.30 and the data box open. Determine the kinetic coefficient of friction m_k as follows.

Adjust the magnitude of the applied force so that it is just enough to cause the block's acceleration to be non-zero. This should be at F_appl = 14.8 N if the applied force is horizontal. Make sure the force is horizontal. PLAY/STEP the motion up to t = 2.00 s and PAUSE at this time.

From the block's displacement in 2.00 s, determine the block's acceleration using the equation relating displacement, acceleration, and time elapsed for motion with constant acceleration. Compare your result with the value of a_x in the data box.

Apply Newton's second law to the block to calculate the x-component of the net force acting on the block, F_x, from the acceleration and the mass of the block. From this and the value of F_appl,x, calculate the value of the x-component of the friction force, F_fric,x. Compare your result with the value in the data box. There may be a slight difference due to round-off.

Since the block is moving in this case, we are dealing with kinetic friction. Use the equation defining the coefficient of kinetic friction m_s,

F_fric = m_k N, (4)

combined with Expression (3) for N to calculate m_k. Compare your result with the value to which the Kinetic Coefficient of Friction slider is set.

Activity 3. The purpose of this activity is to investigate if the force of kinetic friction and the kinetic coefficient of friction depend on the applied force.

REWIND the applet, and set the magnitude of the applied force to 20.0 N. Keep the applied force horizontal.

Again determine the force of kinetic friction and the kinetic coefficient of friction, using the same procedure as in Activity 2. Are the results the same as before?

Activity 4. The purpose of this Activity is to determine if the magnitude of the force of kinetic friction is proportional to the magnitude N of the normal force or to the weight F_grav = mg of the block.

In order to distinguish between N and F_grav, we must set up a situation in which the two quantities have different values.

To do so, set the magnitude of the applied force to 15.0 N and the direction angle q of the applied force to 30^o. Both from the data box and the free-body diagram, you can see that N < F_grav in this case. This time, we'll pretend we know the kinetic coefficient of friction: 0.24. Make sure the slider is set to this value. However, let's pretend we just don't know whether to multiply it by N or mg to get the magnitude of the force of kinetic friction.

As in Activity 1, derive an expression for N by applying Newton's second law to the block. Again, the vertical component a_y of the acceleration is 0. Thus, as in Eq.(2), the sum of the y-components of all forces acting on the block is 0. However, in the present case, there are three, not two, forces that have a non-zero y-component. The applied force is the third one. Thus, with F_appl,y = F_appl sin q,

N - mg + F_appl sin q = 0(5)

N = mg - F_appl sin q.(6)

Calculate N from Eq.(6), and compare the result to the value in the data box.

Then use Eq.(4) to calculate the magnitude of the force of kinetic friction. Is the result consistent with the value of F_fric,x displayed in the data box?

Now calculate the block's acceleration a_x by applying Newton's second law to the block,

F_appl,x + F_fric,x = F_appl sin q - m_k N = ma_x.(7)

Substitute the given values into Eq.(7), and calculate a_x. Does the result agree with the value in the data box?

Predict the block's displacement Dx during a time interval of 2.00 s. Then PLAY the applet, and check if your prediction agrees with the displacement you observe. If it does, then using N rather than mg in Expression (4) for the magnitude of the force of kinetic friction is the right thing to do. Using mg instead of N in this expression would have resulted in a different value for Dx. You may want to do the calculation.

Activity 5. Design an experiment, to be carried out with the applet, that let's you decide whether Expression (1) for the maximum magnitude of the force of static friction should have N or F_grav on the right-hand side multiplying m_s.

Carry out the experiment.