Sample Problems for Exam 3 - University Physics I | PHYS 2050, Exams of Physics

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X3.

PHYS-205(8) (Kaldon-18454)

Name ______________________________________________

Exam 000 - 100,000 points + 20,000WMU-Spring 2001

(^)
(^) points Book Title ________

This is for Topic 1, not your textbook!

___

Sample – Not a Real Exam

Rev. 10/24/2000.

State Any Assumptions You Need To Make – Show All Work – Circle Any Final Answers Use Your Time Wisely – Work on What You Can – Be Sure to Write Down Equations

Feel Free to Ask Any Questions

2a

2b

2c

2e

1.) Two masses, The (Inclined) Plane Truth (25,000 points)

(^) m 1 (^) and

(^) m 2 , are connected over a real pulley with

moment of inertia,

I

, and radius

R

, and where

(^) m 1 (^) < (^) m 2

. Setup

(^) But Do

Not Solve

(^) the equations from the Free Body Diagrams for (a)

(^) m (^1) , (b)

(^) m 2

and from the Free Rotation Diagram for (c) the pulley.

You must

(e) If this ball rolls into a spring and comes to a stop in 0.280 m, find the spring constantenergy of this ball – both linear and rotational terms. (d) A 5.00 kg ball of radius 0.150 m is rolling along without slipping at 5.00 m/s. Find the total kinetic the equations properly linked with each other.indicate which way the masses and the pulley intend to move, and have

(^) k (^) of the spring.

Physics 205 / Sample Exam 3

Spring 2001

Odds and Ends

(25,000 points)

2.)

(a) A plate of mass m = 5.00 kg has dimensions a = 1.00 m and b = 0.480 m.

Find the center of mass coordinates

(^) x cm (^) and

(^) y cm (^) by integrating

x

M

x dm

cm

z

and

y

M

y dm

cm (^)

z

.

(b) A plate of mass m = 5.00 kg has dimensions a = 1.00 m and b = 0.480 m.

Find the moment of inertia

I

(^) of the plate about an axis along the bottom edge as

shown, by integrating

I

r dm

z^

(^2)

.

(c) A torque

to tighten a bolt consists of a force being applied at a distance from the axis of rotation.

given byAs the bolt gets tighter, it gets harder and harder to turn the bolt, so the torque as a function of angle is

= C



(^) , where C is some constant with appropriate units. If the total work done by applying

(d) Which way does the bolt turn in (c) ifthis torque through two complete revolutions is 1500. J, then find C.

points

(^) into

(^) the paper?

Use Right Hand Rule to explain your

answer. (e) Show that the equation

(^) x(t) = A cos(



t) + B sin(



t) satisfies the rules for Simple Harmonic Motion

(S.H.M.) – that is, show that

(^) a = - C x

, where

C

(^) is some constant you will find.

Physics 205 / Sample Exam 3

Spring 2001

Page 3

Draggin´ Mah Pick ´Em Up Truck (25,000 points)

3.) A rear wheel drive pickup truck (m = 1808 kg) goes from zero to 60 mph (v

f

= 26.8 m/s) in ten seconds flat (



t = 10.00 s). (a) Each tire has a radius of 0.

m. What are



0 (^) and



f?

(b) Find



.

Let the wheels be considered solid disks of radius r(c) Each tire has a mass of 17.0 kg, and the wheels that the tires are mounted on have a mass of 10.0 kg.

(^1) = 0.300 m, and the tires to be thin hoops of radius r

2

= 0.450 m. Find the moment of inertia, I, of the two mounted tires on the rear axle.

Neglect the mass of

(d) What is the torque, the axle itself.

spin (^) , needed to accelerate the rear wheels?

this friction force is applied at a distance r(e) The force that moves the truck forward comes from friction as the wheel turns on the ground. Since

2 (^) from the axle, the tires must be supplying this force as a

torque. Find this torque,

forward

(^). Why don’t

spin (^) and

forward

(^) agree? What is the actual torque that the

engine has to supply?

Physics 205 / Sample Exam 3

Spring 2001

Dive! Dive! Dive!

(25,000 points)

Call the support force on the left F by two struts, 1.20 m apart. Draw the Free Body Diagram and Free Rotation Diagram of the diving board.diving springboard (mass = 20.0 kg), contemplating her next jump. The board is supported at the left end 4.) (a) Wei Lin Shi of the People’s Republic of China, m = 45.0 kg, is standing at the end of 3.00 m long

1 and the support toward the middle F

2

. Assume that the diving

What are the vector support forces, (b) board is completely uniform.

F

(^1) and (c)

F

2 ?

the cable is a composite fiber (Y= 10.1 × 10cam”, where a camera (5.00 kg) was moved on a cable to follow the diver. If (d) One of the cooler technologies at the 1996 Olympics was NBC’s “dive

(^6) N/m², with a radius of 0.

m), what is the strain on the cable while the camera is at rest?

Ignore the

(e) If the length of cable above the camera is 1.125 meters, then how far is the cable stretched? pulley.

Physics 205 / Sample Exam 3

Spring 2001

Page 5

5.) In the movie “Toto, I don’t think we’re in Kansas, anymore…” (25,000 points)

(^) The Wizard of Oz

, Dorothy’s house is lifted up and carried off to Oz by a tornado.

once every two seconds, orThe house has a mass, m = 8540 kg, and a moment of inertia, I = 285,000 N·m². It is whirling around



(^) = 3.14 rad/s. Find (a) L and (b) K for the rotational motion.

(c) What it the total energy of the house as it is spinning at



(^) = 3.14 rad/s, has an altitude of 3000. m and

(e) The collision takes place over 0.0103 seconds. Usefinal speed of the house+witch?house, which is no longer spinning but still falling at 11.5 m/s, collides inelastically with her. What is the(d) The Wicked Witch of the East ( m = 135.5 kg ) is hovering at rest with her broomstick when theis falling at 11.5 m/s?

(^) impulse

(^) to find the force on the Wicked Witch of

the East from the collision.

If you didn’t get an answer to (d), use v

f for the witch as 11.5 m/s.

Physics 205 / Sample Exam 3

Spring 2001

Odds and Ends

(25,000 points)

6.)

(a) A plate of mass m = 5.00 kg has sides a = 0.480 m. Find the center of

mass coordinates

(^) x cm (^) and

(^) y cm (^) by integrating

x

M

x dm

cm

z

.

(b) A plate of mass m = 5.00 kg has dimensions a = 0.480 m. Find the moment

of inertia

I

(^) of the plate about an axis along the bottom edge as shown, by

integrating

I

r dm

z^

(^2)

.

(c) An solid disk of mass 71.3 kg and radius 1.21 m has a motion that follows the following equation.

Find the angular acceleration,



,

at time t = 1.00 sec.

( )

.. /. /. /. /. /

t

rad

rad s

rad s

rad s

rad s

rad s

    

(^2) (^2)

(^3) (^3)

7 (^7)

8 8

t

t

t

t

t

(d) Find the torque vector

at t = 1.00 sec.

Use Right Hand Rule to explain your answer.

(e) A torque

to tighten a bolt consists of a force being applied at a distance from the axis of rotation.

given byAs the bolt gets tighter, it gets harder and harder to turn the bolt, so the torque as a function of angle is

= C



², where C is some constant with appropriate units. If the total work done by applying

this torque through two complete revolutions is 1500. J, then find C.

Physics 205 / Sample Exam 3

Spring 2001

Page 7

Mars

(25,000 points)

What is the orbital speed of the satellite in (c) m/s and (d) the angular speed in rad/s?Calculate the acceleration due to gravity at this altitude.(b) The Mars Observer satellite ( m = 227 kg) is in a circular orbit 111 km above the surface of Mars.has a weight of 981 N on the surface of the Earth. What would their weight be on the surface of Mars? 7.) The planet Mars has a radius of 3398 km and a mass of 6.57 × 10²³ kg. (a) An astronaut in a spacesuit

If you didn’t get an

answer to (b), use a

c = g/4 = 2.45 m/s².

(e) The general solution to the Simple Harmonic Oscillator problem is

(^) x(t) =

(^) A sin(



t) + B cos(



t).

Consider our satellite going around Mars in the

(^) x-y

(^) plane. Find the value of the constants

A

(^) and

B

(^) which

describe

(^) x(t)

, for when the satellite is at

(^) x = 0

(^) and

(^) t = 0

(^) as shown.

Physics 205 / Sample Exam 3

Spring 2001

Page 8

From the Days of Chivalry and Knights Errant (25,000 points)

the left. Find (a) the tension in the cable,that attaches to the middle of the drawbridge. There is no support onlowered over a moat. It is held up by a hinge at the right and a cable 8.) A drawbridge, 8.00 m long and with a weight of 2350 N, is

T

(^1) , and (b) the force,

F

1 ,

supplied by the hinge.

across the bridge. Explain (briefly!!!) what happens to(c) A bunch of knights in armor and their horses come clomping

T

1 (^) and

F

1 (^) as

the loading on the bridge continues.

(d) Set up

(^) but do not solve

(^) the equations for where the drawbridge is

raised at a 40° angle, where the cable is 10° off from vertical.

(e) The 4.00 meter long cable (

Y

m (^) = 13.5 × 10

10 N/m² )^

(^) is stretched by 4.00 × 10

m by the tension force^

found in part (a). What is the diameter of the cable?

If you didn’t get the answer in (a), use T

1 (^) = weight

of the drawbridge.