Mass hanging from a rope

1. A mass is hung from ropes as shown in the diagram. The rope on the left has a tension T1 = 10.0 N. (A) Draw a free-body diagram of the knot where the three ropes meet. (B) Find the tension T2 in the right-hand rope. (C) Find the mass which is hanging. (Answers: T2 = 27.5 N, m = 2.98 kg.)

2. A 63.0 kg sprinter starts a race with an acceleration of 4.20 m/s^2. What is the net external force on him?

3. What net external force is exerted on a 1100 kg artillery shell fired from a battleship if the shell is accelerated at 2.40 x 10^4 m/s^2? What force is exerted on the ship by the artillery shell?

4. A motorcycle can produce an acceleration of 3.50 m/s^2 while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, total 400 N. The total mass, including rider, is 245 kg. Draw the necessary free-body diagram. What force does the ground exert forward on the motorcycle to produce its acceleration? How does this relate to the force that the motorcycle exerts backward on the ground?

5. The wheels of a midsize car exert a combined force of 2100 N backward on the road to accelerate the car in the forward direction. Draw a free-body diagram of the car. If the force of friction including air resistance is 250 N and the acceleration of the car is 1.80 m/s^2, what is the mass of the car including its occupants?

6. The weight of an astronaut plus his space suit on the moon is only 60.0 lb. How much do they weigh (in pounds) on the earth?

7. Suppose the mass of a fully loaded module in which astronauts take off from the moon is 10,000 kg. The thrust of the engines is 30,000 N. (A) Calculate its acceleration in a vertical take-off from the moon. (B) Could it lift off from the earth? If not, why not? If so, calculate its acceleration.

8. Show that the acceleration of any object down an incline where friction behaves simply (that is, where f_k = u_k N) is
a = g(sin(theta) - u_k cos(theta)).

Note that this expression is independent of mass. In the Projectile Motion lab, we assert that the acceleration of the puck is a = g sin(theta). Is this consistent with the above equation? (Note: "show" means "derive". You will start with a free-body diagram, obtain a second-law equation, and solve for the acceleration.)

9. Calculate the force a mother must exert to hold her 12.0-kg child in an elevator under the following conditions: (A) The elevator accelerates upward at 0.850 m/s^2. (B) The elevator moves upward at a constant speed of 2.0 m/s. (C) The upward bound elevator slows at a rate of 2.30 m/s^2.

A free-body diagram is necessary for solving this problem. It is the same for all three parts.

10. Two men are pushing a Pontiac (automobile) on level ground. Harry pushes with a force of 300 N, while Bert pushes with a 400 N force. (Both forces are horizontal). The car's mass is 1200 kg, and it is moving at a constant velocity of 2.5 m/s. (A) Draw a free-body diagram of the car, labeling all forces. (B) Calculate the force of friction. (This is not sliding friction: the coefficient of friction is not involved.) (C) Suppose that Harry stops pushing. What is the acceleration of the car? Give the magnitude and direction. (D) Suppose both men stop pushing. What is the acceleration of the car now? (Again, give magnitude and direction.)
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