PHY 1053C -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. The 3 kg block in the figure is free to slide without friction on the 15 degree incline shown below. An external force of 20 N is applied to the block in the horizontal direction.

a) What is the normal force acting on the block?

b) Calculate the acceleration of the block along the incline. Be sure to indicate the direction of the acceleration (a drawing of your coordinate axes with the positive directions clearly shown will help).

c) Calculate the acceleration if the 3 kg block is replaced by a 8 kg block.

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 65 kg man being raised on a platform by cables as shown. Notice that the angle between the platform and the cables is different for each cable and the cables exert no forces directly on the man. The platform is slowly being raised by a crane so it accelerates upward at 3 m/s2.

.

a) Draw an FBD for the man.

b) Calculate the normal force acting on the man.

c) Now the man falls off of the platform, which is 125 kg. If it still accelerates at the same rate as before, find the tension in the wires securing the platform. A new FBD may be helpful in your solution!