Tina have taken a job with a theater company and she is in charge of setting up the props. The props are transported in crates by a truck. The crates are unloaded by being pushed down a ramp. She realizes that the frictional force is making her job difficult, so she decides to investigate how to reduce the frictional force. She is interested in determining how the kinetic frictional force depends on the normal force acting on an object. As a first step, she decides to vary the normal force by changing the angle of the ramp

Equipment

friction block, aluminum sheet, masses and wood blocks

1. Make a sketch of the friction block sliding down the inclined track. Draw and label vectors to indicate the direction of the velocity and the direction of the acceleration. Also assign a symbol to the mass of the block and label it on the drawing.
2. Draw a free-body diagram of the forces on the block as it slides down the ramp. Draw the acceleration vector for the block near the free-body diagram. Choose a coordinate system, and draw the force vectors on the coordinate system (a force diagram). What angles between the force vectors and coordinate axes are the same as the angle between the ramp and the table? Determine all of the angles between the force vectors and the coordinate axes.
3. Write down Newton's 2nd law in both the x and y directions. For any forces that are at an angle to coordinate system, be sure to consider the components along the x and y axes. Make sure that all of the signs are consistent. the answer will depend on how to define the coordinate system.
4. Using the equations in step 3, determine an equation for the normal force in terms of quantities know or can measure (the mass of the friction block, the angle of the track, and g).
5. Using the equations in step 3, determine an equation for the magnitude of the kinetic frictional force on the block in terms of quantities know or can measure (the mass of the block, the angle of the track, g, and the acceleration of the block). How will she obtain the value of the acceleration from the video analysis software?
6. In this problem, she will change the normal force on the block by changing the angle of the track (keeping the mass of the block constant). If increasing the angle of the track, does the normal force on the block increase or decrease? Use the equation for the normal force from question 4 to explain the reasoning. What happens to the kinetic frictional force?
7. The normal force and the kinetic frictional force can also be related using a coefficient of kinetic friction (k). What is this relationship? Use the equation to sketch a graph of the magnitude of the kinetic frictional force on the block as a function of the magnitude of the normal force. How could she determine the value of k from this graph?

Prediction

Sketch a graph of the magnitude of the kinetic frictional force on the sliding block as a function of the magnitude of the normal force.

Does the kinetic frictional force on the block increase, decrease, or stay the same as the normal force on the block increases? Is the relationship linear, or curved? Explain the reason.