PHY 2048C -Newton's Laws Practice

1. Consider the system of weights shown below. Note that the double-sided ramp is frictionless and the rope connecting m1 and m2 is massless.

a) Draw a free body diagram for each of the masses.

b) Calculate the normal force on each of the blocks.

c) Find the tension in the rope and the acceleration of each block.

2. A 700 kg elephant is hung over the side of a building by attaching it to a cable which is secured to a 1000 kg block which can slide along on the rooftop. The coefficients of friction are 0.5 (static) and 0.2 (kinetic) between the block and roof. A man pushes the block 3000 N to the left as shown.

a) Draw a free body diagram for each of the bodies.

b) Find the acceleration of the elephant and tension in the cable.

c) What is the frictional force on the block?

d) Find the acceleration of the elephant and tension in the rope if the man at the top of the building no longer pushes on the block (i.e., if Fext = 0).

3. A popular amusement park ride consists of a 400 kg car (including the rider inside) attached to a rotating rod by a massles cable, as shown below. As the car swings in uniform circular motion, it swings out from the rod so that the cable makes an angle of 30 degrees with the vertical. Assume that the center of the car is 8 m from the center of the rotating rod and that the car makes one full rotation in 10 s.

a) Find the speed of the car around the circle.

b) Calculate the y-component of the tension in the rope.

c) Calculate the x-component of the tension in the rope.

d) If the rope has a strength of 5,000 N, then find the maximum speed the car can move (in a circle) so that the rope does not break.

4. Consider the system of blocks tied together by a string shown in the diagram below. Note that the external force is applied horizontally to the left. All surfaces are frictionless. Use g=10 m/s2.

a) Draw free body diagrams for this system.

b) Calculate the normal force from the inclined plane, the tension in the string, and the acceleration of the block. Be sure to indicate the direction of motion.

5. A 3 kg light fixture is hung in an elevator using two symmetrically placed wires as shown below.

a) If the elevator is stationary, calculate the magnitude of the tension in the wires.

b) What is the tension in the wire if the elevator is accelerating upward at 8 m/s2, then what is the magnitude of the tension in the wires?

6. In the following problem, find the tension in the rope, the frictional force, and the acceleration of the blocks for the two values of the external force shown below. Note that the coefficients of friction are between m1 and the table and the force is applied to m1 horizontally to the left. Be sure to indicate the direction of the acceleration and frictional force.

a) Fext = 20 N.

b) Fext = 40 N.

7. Consider the rollercoaster loop shown below.

The 200 kg car enters the loop of radius 10 m going 20 m/s. Answer the following questions assuming the car is at the position where it enters the loop as shown. Neglect friction.

a) Draw a free body diagram for the car.

b) What is the centripetal acceleration of the car?

c) Calculate the normal force acting on the car.

8. Consider the popular Buccaneer ride shown below. A 80 kg man stands on a platform which is located 4 m from the pivot point and hung by massless cables (the cables make a 60 degree angle with the surface of the platform). The platform is swung in part of a circle at a speed of 6 m/s. For this problem assume you are examining the forces when the platform is at the lowest point in it's motion, when the top of the platform is horizontal.

a)Draw a free body diagram for the man.

b)Calculate the normal force acting on the man.

c) The platform and the man have a mass of 200 kg. Now find the tension in the cable assuming you can treat the man and the platform as a single object. A new FBD will be helpful.