Your Name: _______________________ PHY203

Exam #3

Chapters 8-10

Fri., 4/16/10

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

1-10 _________________ (out of 60)

11 _________________ (out of 40)

Score _______________

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

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

1. Let the vector A = – 4j and B = 3j. Find the vector A x B:

a. 0

b. -12i

c. +12i

d. -12k

e. +12k

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

a. 0

b. -12i

c. +12i

d. -12k

e. +12k

3. Let the vector A = 5i – 4j and B = -3i + 2k. Find the vector A x B:

a. -8i -10j - 12k

b. -8i -10j + 12k

c. -8i +10j - 12k

d. -8i +10j + 12k

e. +8i +10j + 12k

4. A hoop is lying on a horizontal table while it is spinning. Looking down on the table from above, the hoop is spinning in a counterclockwise direction. Find the direction of the angular momentum vector:

a. Out of the table (towards the observer)

b. Into the table (away from the observer)

c. Neither a. nor b.

d. Not enough information is given.

5. Find the kinetic energy of a solid cylinder with mass=3kg and radius=2m which is rolling without slipping with a center-of-mass velocity of 4 m/s:

a. 6 J

b. 12 J

c. 24 J

d. 36 J

e. 48 J

For problems 6 and 7,

6. A hoop of mass 4kg and radius 1.0m is rotating with an angular speed of 3rad/s. A blob of clay of mass 0.5kg is dropped onto the rim of the hoop from above and sticks to the hoop. Find the magnitude of the angular momentum of the hoop-putty system before the putty has stuck to the hoop:

a. 33.0 kgm²/s

b. 4.0 kgm²/s

c. 6.0 kgm²/s

d. 12.0 kgm²/s

e. 48.0 kgm²/s

7. Find the magnitude of the angular velocity of the hoop-putty system after the putty has stuck to the hoop:

a. 0.89 rad/s

b. 2.67 rad/s

c. 3.0 rad/s

d. 3.43 rad/s

e. 10.7 rad/s

For problems 8-10,

Point masses are placed as follows along the x-axis: 1kg at x=0, 2kg at x=1m, and 3kg at x=2m, all connected by a massless rod.

8. Find the x position of the center of mass:

a. 0

b. 1.33m

c. 1.5m

d. 1.6m

e. 2.33m

9. Find the moment of inertia about the x-axis:

a. 0 kgm²

b. 8.0 kgm²

c. 9.0 kgm²

d. 14.0 kgm²

e. 15.0 kgm²

10. Find the moment of inertia about the y-axis:

a. 0 kgm²

b. 8.0 kgm²

c. 9.0 kgm²

d. 14.0 kgm²

e. 15.0 kgm²

11. A 4.0kg pendulum bob at the end of a string of length L=0.5m is released from some angle such that just as it reaches the bottom of its trajectory it has a speed of 1.5m/s. At this point, the 4.0 kg bob collides with a ball of mass 5.0kg and speed 5.0m/s, as shown above. The two balls stick together and swing up to the right. Use g=9.81m/s².

a. Calculate the initial linear momentum of the two ball system just before the collision and express it in vector notation using the coordinate system above.

b. Calculate the initial kinetic energy of the two-ball system just before the collision.

c. Calculate the linear momentum of the two-ball system just after the collision before the balls start to swing up and express it in vector notation using the coordinate system above.

d. Calculate the velocity of the two-ball system just after the collision before the balls start to swing up and express it in vector notation using the coordinate system above.

e. Calculate the kinetic energy of the two-ball system just after the collision before the balls start to swing up.

f. Is the collision elastic or inelastic or can you not tell?

g. Calculate the height, H, of the two-ball system when it stops (momentarily) at the highest point.

h. Find the angle, q, the string makes with the vertical at that height, H.