*PLEASE SOLVE #6*
- Make a sketch of a wood 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.
- 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 your coordinate system (a force diagram). What angles between your force vectors and your 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.
- Write down Newton’s 2nd law in both the x and y directions. For any forces that are at an angle to your coordinate system, be sure to consider the components along the x and y axes. It is also important to make sure that all of your signs are correct. For example, is the acceleration of the block positive or negative? You answer will depend on how you define your coordinate system.
- Using the equations in step 3, determine an equation for the normal force in terms of quantities you know or can measure (the mass of the block, the angle of the track, and g).
- Using the equations in step 3, determine an equation for the magnitude of the kinetic frictional force on the block in terms of quantities you know or can measure (the mass of the block, the angle of the track, g, and the acceleration of the block). How will you obtain the value of the acceleration from the video analysis software?
- In this problem, you will change the normal force on the block by changing the mass of the block (keeping the angle of the track constant). If you increase the mass of the block, does the normal force on the block increase or decrease? Use your equation for the normal force from question 4 to explain your reasoning. What happens to the kinetic frictional force?
- The normal force and the kinetic frictional force can also be related using a coefficient of kinetic friction (??μk). 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 you determine the value of μk from this graph?