1. An object is at rest on a flat, rough, horizontal surface. Compare the horizontal force needed to move the object from rest to the horizontal force needed to keep the object moving with constant velocity once the object is moving.
2. Consider an object placed on an incline. The incline is a flat, rough surface and is inclined at an angle of $\theta$ relative to the horizontal. Draw a free body diagram showing all forces acting on this object.
3. In the previous question, what is the angle between the normal(perpendicular) to the incline and the gravitational force?

Your team has navigated to the bottom of the cliff successfully but are confronted by an incline followed by a tunnel that then leads to the dimensional gate that you might be able to use to get back home. Your amazing piece of tech (turning out to be very useful) indicates that the dimensional gate is at the end of the tunnel. The gate must be entered at a speed of 20mph. It also indicates the angle and height of the incline and the length of the tunnel as displayed in the following screenshot from your tech. The tech also indicates that the base of the tunnel is made of a different surface than that of the incline. Your tech indicates that the incline is made of Leannium and you have conducted previous tests on this material that indicate that a sled can rest on an incline of the material without sliding as long as the angle of the incline is less than or equal to 14º. At the top of the incline are two sleds. You also still have your trusty stopwatch. You have one chance of escape, for all of your group members to push the sled down the incline and get in, move through the tunnel, and then the dimensional gate. You additionally want to bring back information about the frictional properties of these materials. Will you be successful?

Learning Goals Week 5

There are a couple of different approaches to solving the previous part of this problem. If you did not find coefficients of friction in the previous part do this now. Start with ramp, and work in variables only until you are ready to calculate your coefficient. Once you have done this, find the coefficient of friction in the tunnel (HINT: use the variable expression from the ramp here as a starting point). If in completing the previous part you did so but did not find an expression for the coefficient of friction exclusively in variables, redo it now and find an expression for the friction coefficient on the ramp in variable form then use this expression as a starting point for the friction coefficient in the tunnel.

Wrap up Questions:

1. Does the frictional force depend on the mass of the object? What about the contact area? Why?
2. Is this problem mass-dependent?
3. How does the kinetic coefficient differ from the static coefficient of friction? Why are they different? What is happening microscopically?
4. Is your calculated initial velocity reasonably attainable? How do you know?
5. Can you draw free-body diagrams of the cart when it is on the ramp and also on the ground?