Practice Exam 3 - University Physics I | PHYS 2050, Exams of Physics

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X3.7e

PHYS-205(7) (Kaldon-21297)

Name ______________________________________________

Exam 3 - 100,000 points + 20,000WMU - Winter 2001

(^)
(^) points

http://homepages.wmich.edu/~kaldon/

3/28/2001•Rev.4 · 3/21/

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.) (a) A bucket ( m = 5.00 kg ) is hanging at rest from a 1.00 m length of cable ( Y = 10×10 Spinning and Falling and Crashing and Spilling… (50,000 points)

10 N/m² ,^

square cross-section A = 4.00 × 10

m² ). How much does the cable stretch?^

(c) Find the acceleration of the bucket if the brake on the cylinder is released.Free Body Diagram of the bucket and the Free Rotation Diagram of the cylinder.(b) The cable is wrapped around a solid cylinder ( m = 12.5 kg , R = 0.200 m ). Draw the

We are neglecting the mass

of the cable in this problem

.

(e) What is the angular speed of the cylinder just before the bucket hits the ground?ground.the unwinding cable does not slip on the cylinder, find the speed of the bucket just before it hits the(d) The bucket starts off at rest 12.5 meters above the ground. If the brake on the cylinder is released and

Physics 205 / Exam 3

Winter 2001

Page 2

We’re A Bit Off-Center Here Today

(25,000 points)

2.)

(a) A plate of mass

(^) m (^) has sides of

(^) 4a (^) and

(^) 7a

. Find the center of mass

coordinates

(^) x cm (^) by integrating

x

M

x dm

cm (^)

z

, using the

(^) x- (^) and

(^) y- axes as

shown.
(b) A plate of mass

(^) m (^) has sides of

(^) 4a

(^) and

(^) 7a

. Find the moment of inertia

I

(^) of the plate about the

(^) x- axis 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

F = Charder and harder to turn the bolt, so the force as a function of angle is given byof 30.0 cm (0.300 m) from the axis of rotation. As the bolt gets tighter, it gets

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

(d) Which way does the torquefind C.done by applying this torque through two complete revolutions is 1500. J, then

in (c) points?

Use Right Hand Rule to explain your answer.

(e) Show that the equation



(t) = A cos(



t) + B sin(



t) satisfies the rules for a rotational Simple

Harmonic Motion (S.H.M.) – that is, show that



= - C

, where

C

(^) is some constant you will find.