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acceleration and force

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Could you please provide the answers and workings out to the following physics problems. explain exactly how you came up with answer, provide a graph/drawing where needed for better understanding of the answer.

Please see attachment.

1. When the net force that acts on a hockey puck is 10 N, the puck accelerates at a rate of 50 m/s^2. Determine the mass of the puck.

2. A 15-N net force is applied for 6.0 s to a 12-kg box initially at rest. What is the speed of the box at the end of the 6.0-s interval?

3. A 810-kg car accelerates from rest to 27 m/s in a distance of 120 m. What is the magnitude of the average net force acting on the car?

4. Two forces act on a 16-kg object. The first force has a magnitude of 68 N and is directed 24 degrees north of east. The second force is 32 N, 48 degrees north of west. What is the acceleration of the object resulting from the action of these two forces?

5. Two forces act on a 4.5-kg block resting on a frictionless surface as shown. What is the magnitude of the horizontal acceleration of the block?

A 70.0 kg astronaut pushes to the left on a spacecraft with a force F in gravity free space. The spacecraft has a total mass of 1.0 x10^4 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36 m/s^2.
6. Which one of the following statments concerning this situation is true?
7. Determine the magnitude of the acceleration of the spacecraft.

8. Two point masses m and M are separated by a distance d. If the distance between the masses is increased to 3d. how does the gravitational force between them change?

9. An astronaut orbits the earth in a space capsule whose height above the earth is equal to the earth's radius. How does the mass of the astronaut in the capsule compare to her mass on the earth?

10. What is the magnitude of the gravitational force acting on a 79.5-kg student due to a 60.0 kg student sitting 2.25 m away in the lectrue hall?

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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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