ForcesMidterm Practice Part 2
Now that we have done a bunch of friction problems before in Part 1, let’s look at some other types of problems. Remember, the midterm will consist of 3 problems…
1. Here is a problem that might come in handy some day.Suppose you driveyour new Bugatti Veyron into a snow bank and get stuck. Fortunately, you have a length of chain in your boot.*You connect the chain from the tow hitch to a tree. You (who now have a mass of 75 kg, “Freshman 15” and all that) proceed to sit on the middle of the chain as shown, so that the chain makes an angle of 2.5o from the horizontal on each side.
A) How hard will the chain pull on your car? In other words, what is the force of tension FT in the chain? Surprisingly, it turns out that the tension will be much bigger than your weight. To see why, use the 3 Step Plan…
Step 1: Draw the 3 forces on you, including both tensions, which are equal in magnitude. Don’t draw a normal force: just draw the 2 tensions as if they are acting onyour center.
Step 2: Find Fnetgraphically. Indicate θ on your diagram. (What should Fnet be? In other words what is aif you remain at rest?) Note: this Step 2 looks a little different from what you are used to: just go with it!
Step 3: Use your triangle and trig to find FTin terms ofyourmass m. Lastly, plug in the #’s.
2. Here is a question based on a student’s queryin class. Suppose that you (mu = 75 kg) were to step off a table-top located 0.78 m above the surface of the Earth and free-fall to the ground. (The mass of Earth is mE = 6.0 x 1024 kg.) Label the 3rd Law forces acting on you and the Earth…
A) Find the force on you by the Earth. Hint: it is green!
B) Find the force on the Earth by you (3rd Law).
Hint: it is also green!
C) What will the acceleration of the Earth be?
(Apply Newt’s 2nd Law to the Earth.)
D) How long will it take you to fall to the Earth? (You can safely ignore the motion of the Earth to find this time.)
E) How far will the Earth “fall” upward in the time it takes you to fall? Yes, it’s small, but it is the principle of the thing that counts!)
3. Consider the cross section of an ideally banked turn. An ideally banked turn doesn’t require any friction for a vehicle to complete a turn of radius R when the vehicle is traveling at the ideal speed v. (A bowling ball could execute an ideally banked turn if traveling at the ideal speed.) Apply the 3 Step Plan to work your way through this problem to find the ideal banking angle θ.
Step 1: Draw all the forces on the truck. Only write down real forces*!
Step 2: To find Fnet, add the forces graphically in a right triangle…and write down Fnet from the trig. Be careful in adding the forces: which direction should Fnetpoint? Hint: Fnetwill point in the direction the truck is accelerating: this direction is not parallel and down the incline! Can you see that Fnetwill point horizontal and to the left?
After making a beautiful right triangle, use trig to find Fnet, and then apply Newt’s 2nd Law.
Step 3: Solve for θ in terms of v and R. Find θ numerically for v = 30 m/s and R = 402 m.
Does θ depend on m? If it did, banked turns would need signs with different speeds for different vehicles.
1