# Several mechanics problems.

I would like for you to show me all of your work/calculations and the correct answer to each problem.

38. In an emergency stop to avoid an accident, a shoulder-strap seat belt holds a 60-kg passenger firmly in place. If the car were initially traveling at 90 km/h and came to a stop in 5.5 s along a straight, level road, what was the average force applied to the passenger by the seatbelt?

50. Jane and John, with masses of 50 kg and 60 kg, respectively, stand on a frictionless surface 10 m apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of 0.92 m/s[squared] toward him.

(A) What is John's acceleration?

(B) If the pulling force is applied constantly, where will Jane and John meet?

54. A 75.0-kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator is

(a) at rest?

(b) moving up at a constant velocity 2.00m/s

(C) accelerating up at 2.00m/s[squared]

88. A packing crate is placed on a 20-degree inclined plane. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.

42. A 1200-kg automobile travels at a speed of 90 km/hr.

(a) What is its kinetic energy?

(b) What is the net work that would be required to bring it to a stop?

44. A 3.0-g bullet traveling at 350 m/s hits a tree and slows down uniformly to a stop while penetrating a distance of 12 cm into the tree's trunk. What was the force exerted on the bullet in bringing it to rest?

66. A person standing on a bridge at a height of 115 m above a river drops a 0.250 kg- rock.

(A) What is the rock's mechanical energy at the time of release relative to the surface of the river?

(B) What are the rock's kinetic, potential, and mechanical energies after it has fallen 75.0 m?

(C) Just before the rock hits the water, what are its speed and total mechanical energy?

(D) Answer parts (A) to (C) for a reference point (y = 0) at the elevation where the rock is released. (Neglect air resistance.)

76. A 1.5-kg box that is sliding on a frictionless surface with a speed of 12 m/s approaches a horizontal spring. The spring has a spring constant of 2000 N/m.

(A) How far will the spring be compressed in stopping the box?

(B) How far will the spring be compressed when the box's speed is reduced to half of its initial speed?

88. A 60-kg woman runs up a staircase 15 m high (vertically) in 20 s.

(A) How much power does she expend?

(B) What is her horsepower rating?

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the solution is 9 pages long including full explanations, derivations, diagrams and equations dealing with a range of common topics in Newtonian mechanics.

Newtonian Mechanics Problems Involving Rotation

1) The tub of a washer goes into its spin-drycycle, starting from rest and reaching an angular speed of 7.8 rev/s in 3.4 s . At this point the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 15.1 s .

Through how many revolutions does the tub turn? Assume constant angular acceleration while it is starting and stopping.

Answer in units of rev.

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2)

a. A race car starts from rest on a circular track of radius 256 m. The car's speed increases at the constant rate of 0.384 m/s^2. At the point where the magnitudes of the radial and tangential accelerations are equal,determine the speed of the race car. Answer in units of m/s

b. Find the distance traveled at the same moment. Answer in units of m

c. Find the elapsed time at the same moment. Answer in units of s

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3)

a. A small turtle, appropriately named "Dizzy", is placed on a horizontal, rotating turntable at a distance of 16.3 cm from its center. Dizzy's mass is 66.6 g, and the coefficient of static friction between his feet and the turntable is 0.43. Find the maximum angular velocity the turntable can have if Dizzy is to remain stationary relative to the turntable. The acceleration of gravity is 9.8 m/s^2. Answer in units of rev/s

b. The turntable starts from rest at t = 0, and has a uniform acceleration of 1.21 rad/s^2. Find the time at which Dizzy begins to slip.Answer in units of s

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4) Consider a thin 8 m rod pivoted at one end. A uniform density spherical object (whose mass is 8 kg and radius is 1.3 m) is attached to the free end of the rod and the moment of inertia of the rod about an end is Irod =1/3 mL^2 and the moment of inertia of the sphere about its center of mass is Isphere =2/5 mr^2.

What is the angular acceleration of the rodimmediately after it is released from its initial position of 64_ from the vertical? The acceleration of gravity g = 9.8 m/s^2 .

Answer in units of rad/s^2

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5) 1. A wheel of radius 4 m, mass 78 kg, and moment of inertia 34 mr^2 about the center of mass is mounted on a frictionless horizontal axle as shown in the figure. A light cord wrapped around the wheel supports an object of mass twice that of the pulley. The weight is released from rest at the level of A and falls a distance 89 m, past level B.

Find its speed as it passes by the level of B, where the vertical distance AB is 89 m. The acceleration of gravity is 9.8 m/s^2 . Answer in units of m/s

2. Determine the tension of the string. Answer in units of N

6) Consider the setup shown, where the inclined plane has a frictionless surface. The locks have masses m2 and m1. The pulley has mass m3, and is a uniform disc with radius R. Assume the pulley to be frictionless.

What is the acceleration of the blocks? Assume the mass m1 is more massive and is

descending with acceleration a. The moment of inertia of a disk is ½ M R^2. The acceleration of gravity is 9.8 m/s^2. Answer in units of m/s^2