# Equilibrium: Contact Force and Tension in the Ring.

Three identical steel balls, each of mass m, are placed in a cylindrical ring which rests on a horizontal surface and whose height is slightly greater than the radius of the balls. The diameter of the ring is such that the balls are virtually touching one another. A fourth identical ball is then placed on top of the other three. Determine the force, P, exerted by the ring on each of the three lower balls.

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Three identical steel balls, each of mass m, are placed in a cylindrical ring which rests on a horizontal surface and whose height is slightly greater than the radius of the balls. The diameter of the ring is such that the balls are virtually touching one another. A fourth identical ball is then placed on ...

#### Solution Summary

Three balls are kept together by a ring with a fourth ball on top, the force exerted by the ring on three lower balls are calculated.

Newton's Law of Motions: Sample Questions

The following questions and problems are from "Physics 7th edition by Cutnell and Johnson, Chapter 4" which includes the concepts like Newton's laws of motion, the vector nature of Newton's second law of motion, type of forces (gravitational, normal, static and kinetic/frictional forces, tension force), equilibrium and non-equilibrium applications of Newton's laws of motion.

Please consider significant figures and if possible, draw visual graphics.

Conceptual Questions:

1. Why do you lunge forward when your car suddenly comes to a halt? Why are you pressed backward against the seat when your car rapidly accelerates? In your explanation, refer to the most appropriate one of Newton's three laws of motion.

2. The net external force acting on an object is zero. It is possible for the object to be traveling with a velocity that is not zero? If your answer is yes, state whether any conditions must be placed on the magnitude and direction of the velocity. If your answer is no, provide the reason for your answer.

3. Is a net force being applied to an object when the object is moving downward (a) with a constant acceleration of 9.80 m/s^2 and (b) with a constant velocity of 9.80 m/s? Explain.

4. A father and his seven year old daughter are facing each other on the ice skates. With their hands, they push off against one another.

(a) Compare the magnitudes of the pushing forces that they experience.

(b) Which one, if either, experiences the larger acceleration? Account for your answer.

5. According to Newton's third law, when you push on an object, the object pushes you back on you with an oppositely directed force of equal magnitude. If the object is a massive crate resting on the floor, it would probably not move. Some people think that the reason the crate does not move is that the two oppositely directed pushing forces cancel. Explain why this logic is faulty and why the crate does not move.

6. When a body is moved from the sea level to the top of the mountain, what changes - the body's mass, its weight, or both? Explain.

7. The force of air resistance acts to oppose the motion of an object moving through the air. A ball is thrown upward and eventually returns to the ground.

(a) As the ball moves upward, is the net force that acts on the ball greater than, less than, or equal to its weight? Justify your answer.

(b) Repeat part (a) for the downward motion of the ball.

8. A person has a choice of either pushing or pulling a sled at a constant velocity. Friction is present. If the angle θ is the same in both cases, does it require less force to push or to pull? Account your answer.

9. Suppose that the coefficients of static and kinetic friction have values such that µs = 1.4 µk for a crate in contact with a cement floor. Does this mean that the magnitude of the static frictional force acting on the crate at rest would always be 1.4 times the magnitude of the kinetic frictional force acting on the moving crate? Give your reasoning.

10. Can an object ever be in equilibrium if the object is acted on by only (a) a single nonzero force, (b) two forces that point in mutually perpendicular directions, and (c) two forces that point in directions that are not perpendicular? Account for your answer.

11. During the final stages of descent, a sky diver with an open parachute approaches the ground with a constant velocity. The wind does not blow him from side to side. Is the sky diver in equilibrium and, if so, what forces are responsible for the equilibrium?

12. A weight hangs from a ring at the middle of a rope. Can the person who is pulling on the right end of the rope ever make the rope perfectly horizontal? Explain your answer in terms of the forces that act on the ring.

Problems:

(Newton's Law of Motion)

1. A boat has a mass of 6800 kg. Its engines generate a drive force of 4100 N, due west, while the wind exerts a force of 800 N, due east, and the water exerts a resistive force of 1200 N due east. What is the magnitude and direction of the boat's acceleration?

2. A 15-g bullet is fired from a rifle. It takes 2.50 x 10^-3 s for the bullet to travel the length of the barrel with a speed of 715 m/s. assuming that the acceleration of the bullet is constant, find the average net force exerted on the bullet.

(The Vector Nature of Newton's Second Law of Motion and Newton's Third Law):

3. A 350-kg sailboat has an acceleration of 0.62 m/s^2 at an angle of 64 degrees north of east. Find the magnitude and the direction of the net force that acts on the sailboat.

4. When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and, thus, slows him down. Suppose the weight of the sky diver is 915 N and the drag force has a magnitude of 1027 N. The mass of the sky diver is 93.4 kg. What are the magnitude and direction of his acceleration?

(Gravitational Force)

5. A rock of mass 45 kg accidentally breaks loose from the edge of a cliff and falls straight down. The magnitude of the air resistance that opposes its downward motion is 18 N. What is the magnitude of the acceleration of the rock?

6. Synchronous communications satellites are placed in a circular orbit that is 3.59 x 10^7 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?

7. Mars has a mass of 6.46 x 10^23 kg and a radius of 3.39 x 10^6 m.

(a) What is the acceleration due to gravity on Mars?

(b) How much would a 65kg person weigh on this planet?

(The Normal Force, Static and kinetic frictional Force)

8. A block whose weight is 45.0 N rests on a horizontal table. A horizontal force of 36.0 N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and if so, what will be the block's acceleration? Explain your reasoning.

9. A 60.0 kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.760 and 0.410, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?

(The tension Force, Equilibrium Applications of Newton's Law of Motion)

10. A stuntman is being pulled along a rough road at a constant velocity by a cable attached to a moving truck. The cable is parallel to the ground. The mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.870. Find the tension in the cable.

11. A 1.40-kg bottle of vintage wine is lying horizontally in the rack. The two surfaces on which the bottle rests are 90.0 degrees apart, and the right surface makes an angle of 45.0 degrees with respect to the ground. Each surface exerts a force on the bottle that is perpendicular to the surface. What is the magnitude of each of these forces?

(Non-equilibrium Applications of Newton's Law of Motion)

12. The two blocks are connected via a pulley. The weight of the block on the table is 422 N and that of the hanging block is 185 N. Ignoring the frictional effects and assuming the pulley to be massless, find (a) the acceleration of the two blocks and (b) the tension of the cord.

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