Your Name: _______________________ PHY203

Exam #3

Chapters 8-10

Fri., 4/11/08

Lecture Time: 1p.m. 2p.m.

1-10 _________________ (out of 60)

11 _________________ (out of 40)

Total _______________

Multiple choice answer sheet-shade in correct answers below

(one choice per problem):

	1	2	3	4	5	6	7	8	9	10
a
b
c
d
e

1. Masses are placed as follows: 2kg at x=1m and a 2kg rod 1m in length placed along the x-axis from x=0 to x=1m, as shown above. Find the center of mass:

a. 0.25m

b. 0.5m

c. 0.75m

d. 0.67m

e.1.0m

2. A 10kg duck is flying North at 5m/s. A second duck of mass 5kg is flying South at 10m/s. Find the velocity of the center of mass:

a. 0 m/s

b. 0.33 m/s

c. 1.0 m/s

d. 5.0 m/s

e. none of the above

3. A particle of mass 5kg is traveling in a circle of radius 3m at a speed of 2.5m/s. Find the magnitude of the angular momentum:

a. 10.0 kgm²/s

b. 12.5 kgm²/s

c. 37.5 kgm²/s

d. 112.5 kgm²/s

e. none of the above

For problems 4 and 5:

A solid disk of mass 2kg and radius 0.5m is rotating with an angular speed of 5rad/s.

4. Find the moment of inertia about the center:

a. 0.25 kgm²

b. 0.5 kgm²

c. 1.25 kgm²

d. 2.5 kgm²

e. none of the above

5. Find the magnitude of the angular momentum:

a. 0.25 kgm²/s

b. 0.5 kgm²/s

c. 1.25 kgm²/s

d. 2.5 kgm²/s

e. none of the above

6. Let the vector A = 5i – 4j and B = 3j. Find the vector C = A x B:

a. -15k

b. +15k

c. -12i - 15k

d. -12i + 15k

e. 12i - 15k

7. Albert Einstein stands on a platform with his arms extended and holding masses in each hand. The combined moment of inertia of him plus weights in this position is 12kgm². The platform is rotating with an angular speed of 5rad/s. If he brings his arms in towards his body, his moment of inertia drops to 8 kgm². Find his new angular speed:

a. 0.13 rad/s

b. 0.3 rad/s

c. 1.5 rad/s

d. 3.33 rad/s

e. 7.5 rad/s

8. A wheel is spun up from rest with a constant angular acceleration of a=3.5rad/s². Find the angular velocity after 15 sec.:

a. 4.3 rad/sec.

b. 26.25 rad/sec.

c. 52.5 rad/sec.

d. 394 rad/sec.

e. none of the above

9. A disk of mass 10 kg and radius 0.5 m is at rest. A force of 10 N is applied at the

edge of the disk at an angle of 60^o as shown.

Find the magnitude of the torque, t.

a. 2.5 Nm

b. 4.3 Nm

c. 5.0 Nm

d. 10.8 Nm

e. 12.5 Nm

10. Find the kinetic energy of a solid sphere with mass=2kg and radius=1m which is rolling without slipping with a center-of-mass velocity of 5 m/s:

a. 7.0 J

b. 25 J

c. 35 J

d. 37.5 J

e. 50J

11. A 5.0kg block is traveling in the positive x-direction on a horizontal, frictionless

surface at an initial speed of 8.0m/s. The block explodes and breaks into two

pieces. One piece (m₁ = 3.0kg) shoots off in the negative y direction with a speed

of 4.0m/s.

a. Using the coordinate system shown above, calculate the initial momentum

and kinetic energy of the block before the explosion. Write the momentum in vector

notation.

b. Find the momentum of the combined two-block system just after the explosion

and write the momentum in vector notation.?

c. Find the velocity of the second block ( m₂) after the explosion and write it in vector notation.

d. Is the process elastic or inelastic? Prove it quantitatively.

Exam #3

Crib Sheet

Chapters 8-10

center of mass: M_totr_cm = m₁r₁ + m₂r₂+ m₃r₃ + ....

velocity of center of mass: M_totv_cm = m₁v₁ + m₂v₂+ m₃v₃ + ....

F_{net ext} = Ma_cm

momentum: p = mv

Conservation of momentum (net external force = 0): p_initial = p_final

Kinetic energy, K = (1/2)mv² K = (1/2)Iw² for rotating objects

K = (1/2)m v_cm ² + (1/2)Iw² for objects rolling w.o slipping

For objects rolling w.o slipping, : v_cm = wr (cm = center-of-mass)

Gravitational Potential Energy, U = mgh

Impulse: I = Dp = F_avDt

For a vectors A,B,C with magnitude A,B,C and direction:

If C = A x B; C = ABsinq with direction of C given by the right hand rule

i x j = k; j x k = i; k x i = j

moment of inertia: I = mr² for a single particle

torque: t = r x F = Ia

angular momentum: L = r x p or L = Iw where p = mv

parallel axis theorem: I = I_CM + Mh²

For constant angular acceleration:

q = q_o + w_ot + 1/2at²

w = w_o + at

w² = (w_o )² + 2a(Dq)

For rotating objects: v_tan = wr

circumference of a circle = 2pr