Your Name: _______________________ PHY203

Final Exam 3

Chapters 8-10

Mon, 5/9/11

Part 3

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

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. Masses are placed on the x axis as follows: a 1.0 kilogram uniform sphere with its center at x = 0, a 2.0 kilogram uniform sphere with its center at x = 2.0 m, and a uniform 2.0 kilogram rod with a length of 1.0 m placed along the x axis from x = 0 to x = 1.0 m. Find the x position of the center of mass.

a. 0.25 m

b. 0.50 m

c. 0.75 m

d. 1.0 m

e. 1.25 m

2. A crash test car contains a crash test dummy. If the car is moving at a speed of 75 km/h (20.9 m/s) when it crashes into a wall and stops, calculate the magnitude of the total impulse imparted to the 77.3-kg crash test dummy sitting in the automobile during the collision.

a. 1.62x10³

b. 3.24x10³

c. 1.16x10⁴

d. 5.8x10⁴

e. None of the above

3. 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. Assuming the rod-mass combination is rotating about the y-axis with an angular speed of 5rad/s, find the magnitude of the angular momentum:

a. 1.6 kgm²/s

b. 2.8 kgm²/s

c. 40.0 kgm²/s

d. 70.0 kgm²/s

e. none of the above

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

a. 0

b. -12i

c. +12i

d. -12k

e. +12k

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

a. +15i -12j - 10k

b. -15i +12j - 10k

c. -15i -12j -+10k

d. +15i -12j + 10k

e. None of the above

For problems 6-10:

Two pucks collide on a frictionless horizontal surface, as shown below. Before the collision, puck 1 (mass=4kg) is traveling in the positive x-direction with a speed of 3.5m/s and puck 2 (mass=3kg) is traveling in the negative x-direction with a speed of 2.5m/s. After the collision, puck 1 travels off at an angle of 30⁰ with respect to the x-axis at a speed of 3m/s.

6. Find the momentum of puck #2 before the collision.

a. -7.5i kgm/s

b. -2.5i kgm/s

c. +2.5i kgm/s

d. +7.5i kgm/s

e. none of the above

7. Find the total momentum of the system before the collision.

a. +1.0i kgm/s

b. +6.5i kgm/s

c. +15.9i kgm/s

d. +21.5i kgm/s

e. +15.9 kgm/s

8. What is the total momentum of the system after the collision?

a. less than before the collision

b. the same as before the collision

c. more than before the collision

d. not enough information is given

9. Find the x-component of the velocity of puck #2 after the collision.

a. -5.1m/s

b. -1.3m/s

c. +0.1m/s

d. +1.3m/s

e. +5.6m/s

10. Find the y-component of the velocity of puck #2 after the collision.

a. -2.0m/s

b. -1.5m/s

c. +1.5m/s

d. +2.0m/s

e. none of the above

11. A 4.0 kg block is resting on a horizontal, frictionless table, as shown. It is attached to a 6.0 kg block with a massless string. The string passes over an M = 5.0 kg pulley which is a solid disk with a radius of R = 0.5 m. The blocks are released. Use g=9.81m/s².

a. Calculate the moment of inertia of the pulley.

b. Using the symbols m₁, T₁, a, and g , and using the given coordinate system, write out Newton's 2nd Law for block 1 in the x direction.

b. Using the symbols m₂, T₂, a, and g , and using the given coordinate system, write out Newton's 2nd Law for block 2 in the y direction.

d. Using the symbols T₁, T₂, M, R, and a, write out the torque equation for the pulley.

e. Combine the 3 equations to find the linear acceleration of the blocks and the angular acceleration of the pulley.