Assignment 2: Newton's Laws of MotionDue: 2:00am on Saturday, September 11, 2010

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Pulling Three Blocks

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surfaceby a horizontal force . The magnitude of the

tension in the string between blocks B and C is = 3.00 . Assume that each block has mass

= 0.400 .

Part A

What is the magnitude of the force?

Hint A.1 Find the acceleration of block B

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Hint A.2 Find the acceleration of all three blocks

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Express your answer numerically in newtons.

ANSWER: = 4.50

Correct

Part B

What is the tension in the string between block A and block B?

Hint B.1 How to approach the question

Hint not displayed

Express your answer numerically in newtons

ANSWER: = 1.50

=Correct

A Ride on the Ferris Wheel

A woman rides on a Ferris wheel of radius 16 that maintains the same speed throughout its motion.

To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it.When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scalereading versus time. Note that the graph has aminimum value of 510 and a maximum value

of 666 .

Part A

What is the woman's mass?

Hint A.1 How to approach the problem

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Hint A.2 Find the extreme points on the circular path

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Hint A.3 Find the acceleration of the woman

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Hint A.4 Mass and weight

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Express your answer in kilograms.

ANSWER: = 60

Correct

The Window Washer

A window washer of mass is sitting on a platform suspended by a system of cables and pulleys as

shown . He is pulling on the cable with a force ofmagnitude . The cables and pulleys are ideal

magnitude . The cables and pulleys are ideal

(massless and frictionless), and the platform hasnegligible mass.

Part A

Find the magnitude of the minimum force that allows the window washer to move upward.

Hint A.1 Find a simple expression for the tension

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Hint A.2 Upward forces on window washer

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Hint A.3 All forces on window washer

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Hint A.4 What about the platform?

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Express your answer in terms of the mass and the magnitude of the acceleration due to

gravity .

ANSWER:

=

Correct

Skydiving

A sky diver of mass 80.0 (including parachute) jumps off a plane and begins her descent.

Throughout this problem use 9.80 for the magnitude of the acceleration due to gravity.

Part A

At the beginning of her fall, does the sky diver have an acceleration?

Hint A.1 Free fall

Hint not displayed

Hint not displayed

ANSWER:No; the sky diver falls at constant speed.

Yes and her acceleration is directed upward.

Yes and her acceleration is directed downward.

Correct

This applet shows the sky diver (not to scale) with her position, speed, and acceleration graphedas functions of time. You can see how her acceleration drops to zero over time, giving constantspeed after a long time.

Part B

At some point during her free fall, the sky diver reaches her terminal speed. What is the magnitude ofthe drag force due to air resistance that acts on the sky diver when she has reached terminal

speed?

Hint B.1 Dynamic equilibrium

Hint not displayed

Express your answer in newtons.

ANSWER: = 784

Correct

Part C

For an object falling through air at a high speed , the drag force acting on it due to air resistance can

be expressed as,

where the coefficient depends on the shape and size of the falling object and on the density of air.

For a human body, the numerical value for is about 0.250 .

Using this value for , what is the terminal speed of the sky diver?

Hint C.1 Terminal speed

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Express you answer in meters per second.

ANSWER: = 56.0

Correct

Recreational sky divers can control their terminal speed to some extent by changing their bodyposture. When oriented in a headfirst dive, a sky diver can reach speeds of about 54 meters persecond (120 miles per hour). For maximum drag and stability, sky divers often will orientthemselves "belly-first." In this position, their terminal speed is typically around 45 meters persecond (100 miles per hour).

Part D

When the sky diver descends to a certain height from the ground, she deploys her parachute to ensurea safe landing. (Usually the parachute is deployed when the sky diver reaches an altitude of about 900

--3000 .) Immediately after deploying the parachute, does the skydiver have a nonzero

acceleration?

Hint D.1 How to approach the problem

Hint not displayed

ANSWER:No; the sky diver keeps falling at constant speed.

Yes and her acceleration is directed downward.

Yes and her acceleration is directed upward.

Correct

Part E

When the parachute is fully open, the effective drag coefficient of the sky diver plus parachuteincreases to 60.0 . What is the drag force acting on the sky diver immediately after she

has opened the parachute?

Hint E.1 How to approach the problem

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Hint E.2 Find the speed of the sky diver when the parachute is deployed

Hint not displayed

Express your answer in newtons.

ANSWER: = 1.88×105

Correct

Part F

What is the terminal speed of the sky diver when the parachute is opened?

Hint F.1 How to approach the problem

Hint not displayed

Express your answer in meters per second.

ANSWER: = 3.61

Correct

A typical "student" parachute for recreational skydiving has a drag coefficient that gives a terminalspeed for landing of about 2 meters per second (5 miles per hour). If this seems slow based onvideo or real-life sky divers you have seen, that may be because the sky divers you saw wereusing high-performance parachutes; these offer the sky divers more maneuverability in the air but

using high-performance parachutes; these offer the sky divers more maneuverability in the air butincrease the terminal speed up to 4 meters per second (10 miles per hour).

Block on an Incline Adjacent to a Wall

A wedge with an inclination of angle rests next to a wall. A block of mass is sliding down the plane,

as shown. There is no friction between the wedge and the block or between the wedge and thehorizontal surface.

Part A

Find the magnitude, , of the sum of all forces acting on the block.

Hint A.1 Direction of the net force on the block

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Hint A.2 Determine the forces acting on the block

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Hint A.3 Find the magnitude of the force acting along the direction of motion

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Express in terms of and , along with any necessary constants.

ANSWER: =

Correct

Part B

Find the magnitude, , of the force that the wall exerts on the wedge.

Hint B.1 The force between the wall and the wedge

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Hint B.2 Find the normal force between the block and the wedge

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Hint B.3 Find the horizontal component of the normal force

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Express in terms of and , along with any necessary constants.

ANSWER: =

Correct

Your answer to Part B could be expressed as either or . In either

form, we see that as gets very small or as approaches 90 degrees ( radians), the contact

force between the wall and the wedge goes to zero. This is what we should expect; in the firstlimit ( small), the block is accelerating very slowly, and all horizontal forces are small. In the

second limit ( about 90 degrees), the block simply falls vertically and exerts no horizontal force

on the wedge.

Velocity from Force Diagram Ranking Task

Below are birds-eye views of six identical toy cars moving to the right at 2 . Various forces act on the

cars with magnitudes and directions indicated below. All forces act in the horizontal plane and are eitherparallel or at 45 or 90 degrees to the car's motion.

Part A

Rank these cars on the basis of their speed a short time after the forces are applied.

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Summing force vectors

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Rank from largest to smallest. To rank items as equivalent, overlap them.

ANSWER:

View Correct

Mass on Turntable

Mass on Turntable

A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated inthe diagram .The small metal cylinder has a mass of 0.20 ,

the coefficient of static friction between thecylinder and the turntable is 0.080, and thecylinder is located 0.15 from the center of the

turntable.Take the magnitude of the acceleration due togravity to be 9.81 .

Part A

What is the maximum speed that the cylinder can move along its circular path without slipping

off the turntable?

Hint A.1 Centripetal acceleration

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Hint A.2 Determine the force causing acceleration

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Hint A.3 Find the maximum possible friction force

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Hint A.4 Newton's 2nd law

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Express your answer numerically in meters per second to two significant figures.

ANSWER: = 0.34

Correct

Two Blocks and Two Pulleys

A block of mass is attached to a massless, ideal string. This string wraps around a massless pulley

and then wraps around a second pulley that is attached to a block of mass that is free to slide on a

frictionless table. The string is firmly anchored to a wall and the whole system is frictionless.

Use the coordinate system indicated in the figure when solving this problem.

Part A

Assuming that is the magnitude of the horizontal acceleration of the block of mass , what is ,

the tension in the string?

Hint A.1 Which physical principle to use

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Hint A.2 Force diagram for the block of mass

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Express the tension in terms of and .

ANSWER:

=

Correct

Part B

Given , the tension in the string, calculate , the magnitude of the vertical acceleration of the block

of mass .

Hint B.1 Which physical principle to use

Hint not displayed

Hint B.2 Force diagram for the block of mass

Hint not displayed

Express the acceleration magnitude in terms of , , and .

ANSWER:

=

Correct

Part C

Given the magnitude of the acceleration of the block of mass , find , the magnitude of the

horizontal acceleration of the block of mass .

Hint C.1 Method 1: String constraint (uses calculus)

Hint not displayed

Hint C.2 Method 2: Intuition (does not involve calculus)

Hint not displayed

Express in terms of .

ANSWER:

=

Correct

Part D

Using the result of Part C in the formula for that you previously obtained in Part A, express

as a function of .

Express your answer in terms of and .

ANSWER:

=

Correct

Part E

Having solved the previous parts, you have all the pieces needed to calculate , the magnitude of the

acceleration of the block of mass . Write an expression for .

Hint E.1 How to approach this problem

Hint not displayed

Express the acceleration magnitude in terms of , , and .

ANSWER:

=

Correct

Hanging Chandelier

A chandelier with mass is attached to the

ceiling of a large concert hall by two cables.Because the ceiling is covered with intricatearchitectural decorations (not indicated in thefigure, which uses a humbler depiction), the

workers who hung the chandelier couldn't attachthe cables to the ceiling directly above thechandelier. Instead, they attached the cables tothe ceiling near the walls. Cable 1 has tension

and makes an angle of with the ceiling.

Cable 2 has tension and makes an angle of

with the ceiling.

Part A

Find an expression for , the tension in cable 1, that does not depend on .

Hint A.1 Find the sum of forces in the x direction

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Hint A.2 Find the sum of forces in the y direction

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Hint A.3 Putting it all together

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Express your answer in terms of some or all of the variables , , and , as well as the

magnitude of the acceleration due to gravity .

ANSWER: =

Correct

At the Test Track

You want to test the grip of the tires on your new race car. You decide to take the race car to a smalltest track to experimentally determine the coefficient of friction. The racetrack consists of a flat, circularroad with a radius of 45 . The applet shows the result of driving the car around the track at various

speeds.

Part A

What is , the coefficient of static friction between the tires and the track?

Hint A.1 How to approach the problem

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Hint A.2 Use the applet to find the speed

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Hint A.3 Find an expression for

Find an expression for

Hint not displayed

Express your answer to two significant figures.

ANSWER: = 0.91

Correct

Score Summary:

Your score on this assignment is 100%.You received 40 out of a possible total of 40 points.