Physics for Scientist and Engineers third edition Newton’s...

1/27 NewtonsApplicationProblems.pdf (#2)2012-09-14 18:14:12

Newton’s Laws

Example Problem

Our 10.0 kg mystery bx rest on a horizontal floor. The coefficent of static friction is µs= 0.40 and the coefficent of kinetic friction is µk= 0.30. Determine the force of friction Ffr acting on the box if a horizontal external applied Force Fa is exerted on it of magnitude A) 0, B) 10N, C) 20 N D) 38 N E) 40 N

Variables

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Solution

Answer: O, 10 N, 20 N, 38N, 39N, 29N

Physics for Scientist and Engineers third edition

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2/27 NewtonsApplicationProblems.pdf (2/12)2012-09-14 18:14:12

Newton’s Laws

Example Problem

A 10.0 kg box is pulled along a horizontal surface by a force Fp of 40.0 N which is applied at a 30˚ angle. There is now friction. The coefficent of friction µk= 0.30. Determine the acceleration

Variables

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Solution

Answer: 78.0 N, 23.4 N, 34.6N, 1.1 m/s^2


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Newton’s Laws

Example Problem

Two boxes are connected by a cord running over a pulley. Box one (5.0kg) is on the table and Box two (2.0kg) is suspended off of the table. The coefficent of kinetic friction between box 1 and the table is 0.20. We ignore the mass of the cord and pulley and any friction in the pulley, which means we can assume the force applied to one end of the cord will have the same magnitude at the other end. We wish to find the acceleration a of the sytem, which will have the same magnitude for both boxes assuming the cord doesn’t stretch. As box II moves down, Box i moves to the right

Variables

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Solution

Answer: 1.4 m/s^2, 17N


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Newton’s Laws

Example Problem

The skier has begun descending on the 30˚ slope. Assuming the coefficent of kinetic friction is 0.10 calculate a) her acceleration and b) the speed she will reach after 4.0 s

Variables

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Solution

Answer: 0.41g, 16 m/s


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Newton’s Laws

Example Problem

Suppose that in the example previously that the snow is slushy and the skier moves down the 30˚ slope at constant speed. Wht can you say about the coefficent of friction µk.

Variables

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Solution

Answer: 0.58


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Newton’s Laws

Example Problem

A box of mass m1= 10.0 kg rests on a surface inclined at ø= 37˚ to the horizontal. It is connected by a lightweight cord, which passes over a massless and frictionless pulley to a second mass m2, which hangs freely. A) If the coefficent of static friction is 0.40, determine what range of values for mass m2 will keep the system at rest B) If the coefficent of kinetic firction is 0.30 and m2= 10.0 kg, determine the acceeleration of the system

Variables

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Solution

Answer: 0.78 m/s^2


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Newton’s Laws

Example Problem

Estimate the force a person must exert on a string attached to a 0.150 kg ball to make the ball revlove in a horizontal circle of radius 0.600 m. The ball makes 2.00 revolutions per second (T=0.500 s)

Variables

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Solution

Answer: 14 N


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Newton’s Laws

Example Problem

A small ball of mass m suspended by a cord of length L revloves in a circle of radius r=L sin ø, where ø is the angle the string makes with the vertical. A) in what direction is the acceleration of the ball, and what causes the acceleration B) Calculate the speed and period of the ball in terms of L, ø, and m

Variables

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Solution

Answer:


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Newton’s Laws

Example Problem

A 0.150 kg ball on the end of a 1.10 m long cord is swung in a vertical circle. Determine the minimum speed the ball must have at the top of its arc so that it continues moving in a circle B) Calcualte the tension in the cord at the bottom of the arc if the ball is moving at twice the speed of part a

Variables

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Solution

Answer: 7.34 N


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Newton’s Laws

Example Problem

A 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 50 km/h (14 m/s). Will the car make the turn, or will it skid if A) the pavement is dry and the coefficent of static friction is µs= 0.60 B) the pavement is icy and µs = 0.25

Variables

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Solution

Answer: 5900 N, 2500 N


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Newton’s Laws

Example Problem

For a car traveling with speed v around a curve of radius r, determine a formula for the angle at which a road should be banked so that no friction is required. B) What is this angle for an expressway off ramp curve radius 50 m at a design speed of 50 km/h

Variables

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Solution

Answer: 22˚


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Newton’s Laws

Example Problem

A racing car starts from rest in the pit area and accelerates at a uniform rate to a speed of 35 m/s in 11 s, moving on a circular track of radius 500 m. Assuming constant tangential acceleration, find A) the tangential acceleration B) radial acceleration at the instant when the speed is v= 15 m/s and again when v= 30 m/s

Variables

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Solution

Answer: 0.45 m/s^2, 1.8 m/s ^2


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13/27 NewtonsLawProblems.pdf (#1)2012-09-14 18:14:15

Newton’s Laws

Example Problem

Estimate the net force needed to accelerate a) a 1000 kg car at 1/2g; b) a 200 g apple at the same rate

Variables

Drawing

Solution

Answer: 5000N; 1N


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14/27 NewtonsLawProblems.pdf (2/15)2012-09-14 18:14:15

Newton’s Laws

Example Problem

What constant net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a

distance of 55 m

Variables

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Solution

Answer: -7.1 m/s^2, -1.1 E4 N


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Newton’s Laws

Example Problem

A friend has given you a special gift, a box of mass 10.0 kg with a mystery surprise inside. It’s a

reward for your fine showing on the physics final. The box is resting on the smooth (frictionless)

horizontal surface of a table. A) determine the weight of the box and the normal force acting on it

B)Now your friend pushes down on the box with a force of 40.0 N. Again determine the normal force

acting on the box C) If your friend pulls upward on the box with a force of 40.0 N, what now is the

normal force on the box

Variables

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Solution


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Answer: 98.0N; 138.0 N;58.0N

Newton’s Laws

Example Problem

What happens when a person pulls upward on the box from the previous problem part c with a force

equal to, or greater than, the box’s weight, say Fp = 100.0N rather than the 40.0 N

Variables

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Solution


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Answer: 2.0N

Newton’s Laws

Example Problem

A 65 kg woman descends in an elevator that briefly, when leaving a floor, accelerated at 0.20g a)If she

stands on a scale during this acceleration, what is her weight and what does the scale read? B) What

does the scale read when the elevator descends at a constant speed of 2.0 m/s

Variables

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Solution


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Answer: 52kg; 65kg

Newton’s Laws

Example Problem

Calculate the sum of the two forces acting on the boat (F1= 40.0N at 45 degrees above the x) (F2=

30.0N at 37.0 degrees below the x axis)

Variables

Drawing


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Solution

Answer: 53.3 N at 11.0˚

Newton’s Laws

Example Problem

Suppose a friend asks to examine the 10.0 kg box you were given, hoping to guess what is inside; and

you respond, “Sure, pull the box over to you.” She then pulls the box by the attached ribbon, along the

smooth surface of the table. The magnitude of the force exerted by the person is Fp= 40.0N and it is

exerted at a 30.0˚ angle. Calculate A) the acceleration of the box, and B) the magnitude of the upward

force Fn exerted by the table on the box. Assume that friction can be neglected

Variables

Drawing


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Solution

Answer: 3.46 m/s^2; 78.0 N

Newton’s Laws

Example Problem

Two boxes are connected by a lightweight cord and are resting on a smooth table. The boxes have

masses of 12.0 kg and 10.0 kg. A horizontal force Fp of 40.0 N is applied by a person to the 10.0 kg

box. Find A) the acceleration of each box and B) the tension in the cord

Variables


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Drawing

Solution

Answer: 1.82 m/s^2; 21.8 N

Newton’s Laws

Example Problem


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Two masses suspended over a pulley by a cable is sometimes referred to generically as an Atwood’s

machine. Consider the real life application of an elevator (m1) and its counterweight (m2). To

minimize the work done by the motor to raise and lower the elevator safely, m1 and m2 are similar in

mass. We leave the motor out of the system for this calculation, and assume that the cable’s mass is

neglible and that the mass of the pulley, as well as any friction, is small and ignorable. These

assumptions assure that the tension Ft in the cord has the same magnitude on both sides of the pulley.

Let the mass of the counterweight m2= 1000 kg. Assume the mass of the empty elevator is 850kg and

its mass when carrying four passengers is m1= 1150kg. For the latter case (m1=1150kg), calcuate A)

acceleration of the elevator B) Tension in the cable

Variables

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Solution

Answer: 0.68 m/s^2; 10.500 N


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Newton’s Laws

Example Problem

Finding her car stuck in the mud, a bright graduate of a good physics course ties a strong rope to the

back bumper of the car, and the other end to a tree. She pushes at the midpoint of the rope with her

maximum effort, which she estimates to be a force of Fp=300N. The car just begins to budge with the

rope at an angle ø which she estimates to be 5˚. With what force is the rope pulling on the car?

Neglect the mass of the rope

Variables

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Solution


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Answer: 1700N

Newton’s Laws

Example Problem

A small mass m hangs from a thin string and can swing like a pendulum. You attach it above the

window of your car. When the car is at rest, the string hangs vertically. What angle ø does the string

make a) when the car accelerates at a constant a= 1.20 m/s^2 b) when the car moves at constant

velocity, v= 90 km/h

Variables

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Solution


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Answer: 7.0˚; ø=0˚

Newton’s Laws

Example Problem

A box of mass m is placed on a smooth (frictionless) incline that makes an angle ø with the horizontal

A) Determine the normal force on the box B) Determine the box’s acceleration C) Evaluate for a mass

m=10kg and an incline of ø=30˚

Variables

Drawing


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Solution

Answer: 4.9 m/s^2


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