THURSDAY Oct  28th:

Journal:

Review:

1. A hydraulic lift has a 2.0cm diameter input piston that has a force applied to it of 300N. What is the lift force on the other piston (80cm diameter)?

1. F₁/A₁ = F₂/A₂

300/3.14 =  F₂/1600(3.14)

F₂ = 480,000N

2. An object of mass M travels along a horizontal air track at a constant speed  v and collides elastically with an object of identical mass that is initially at rest on the track. Which of the following statements is true for the two objects after the impact?

(A) The total momentum is Mv and the total kinetic energy is ½ Mv².

(B) The kinetic energy of each object is ¼ Mv².

(C) The total momentum is less than Mv and the total kinetic energy is ½ Mv².

(D) The momentum of each object is ½ Mv.

(E) The total momentum is Mv and the total kinetic energy is less than ½ Mv².

3. Object A of mass M travels along a horizontal air track at a constant speed  V_i and collides

in-elastically with an object B (3 times the mass of object A) that is initially at rest on the track. Object A rebounds backwards at 1/2 V_i.  What is the velocity of the second object after the impact?

2. E

3. M_oi = M_of

M₁V_1i  + M₂V_1i  =  M_1fV_1f  +  M_2V2f

M₁V_1i  + 0  =  -.5(M_1iV_1i) +  3M_1iV_2f

M₁V_1i   =   -.5(M_1iV_1i)  +  3M_1iV_2f

 1.5V_1i   =     3V_2f

V_1i   =     1.5V_2f  

or   V_2f  =  .67V_1i

New material:

4. Increasing the mass M of a mass-and-spring system causes what kind of change on the frequency of the system?

T_s = 1/f  = 2 √ (m/k)

Increasing the mass, decreases the period

Therefore,

The frequency decreases

5. A 10.0 kg object is attached to a spring of spring constant to 4 N/m. The object is displaced by 10.0 cm from the equilibrium position and let go. 

a. What is the period of vibration?

b. What is the frequency?

c. If the object is displaced to 20.0cm, what is now the period of vibration?

a. T_s = 1/f  = 2 p √(m/k)

T_s = 2p √(10/4) =   9.9 s

b. T_s = 1/f  --> f = 1/T_s

   f = 1/9.9s  = .10Hz 

c. displacement has no effect to T or f

T_s = 1/f  = 2 p √(m/k)

T_s = 2p √(10/4) =   9.9 s

6. Decreasing the spring constant k of a mass-and-spring system causes what kind of change in period & frequency of the system?  (Assume no change in the system’s mass m.)

T_s = 1/f  = 2 p √(m/k)

Inverse relationship between period & k

& Direct relationship between f & k

So decreasing the k causes an

increase in the period

& an decrease in frequency.

Free Response Problems: