Physics 207w, w2 (Summer) Exam 2

Lecturer: Min Xu
Rec. Instructor: Jiali Li and Ke Li

July 16, 1998
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ Recitation Section: ______________________________________________________________________________________________

General Instruction

You have 1 hour to answer 4 questions plus one extra credit question on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name and recitation section on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol. The following may be useful:

2 g = 10m/s G = 6.67 × 10-11N . m2/kg2 24 Mearth = 5.97 × 10 kg Rearth = 6.38 × 106m 1atm = 1.01325 × 105P a h = h + w t + 1at2 0 0 2 w = w0 + at 2 2 w = w0 + 2a(h - h0) I = Smr2 2 Ip = Icm + M d L = r × mv L = Iw m1m2 Fg = G ---2-- r U = - Gm1m2--- V ~ r- m T = 2p k- V ~ -- L T = 2p -- V ~ g--- mgd T = 2p ----- V~ -----I-- v20 A = x20 + -2- w v f = arctan(- --0-) wx0

1. A 10.0g bullet with a horizontal speed of 200m/s is fired into a 990g wood block suspended from a string 2.00m long. The wood is at rest initially and the bullet makes a completely inelastic collision with the wood block.
(a) Find the velocity of the block just after the impact of the bullet.
(b) Find the maximum height the block can swing up.
(20 points)

2. A meter stick with a mass M = 2kg is pivoted at one end so it can rotate about a horizontal axis without friction. A small mass m = 1kg is attached on its another end. The stick is held at a horizontal position and then released from rest.
(a) Find the inertia of the system along the axis.
(b) Find the angular velocity of the stick when it passes through the vertical position.
(25 points)

3. A block A with mass mA = 8.00kg is placed on a horizontal surface and is connected to a second hanging block B with mass mB = 6.00kg by a cord passing over a frictionless pulley. The coefficient of kinetic friction is mk = 0.25 between block A and the surface. The blocks are released from rest.
(a) Use the energy method to find the velocity of block B after it descends for 3m. Ignore the mass of the pulley.
(b) If the pulley has radius R = 0.1m and its moment of inertia I = 0.1kg . m2, and assume the cord does not slip over the pulley, find the velocity in part (a) again.
(30 points)

4. A turnable table with radius 2m starts rotation from rest. It has an angular acceleration 0.5rad/s in the first revolution and then the acceleration is off ( it moves at a constant angular velocity ). The moment of inertia of the table along the axis is 60kg . m2.
(a) What is the angular velocity of the table after its first revolution?
(b) When it is in the 3rd revolution, a bag with mass 5kg is dropped onto the rim of the table and then the bag moves with the table. Find that new angular velocity.
(25 points)

5.
(a) [extra credit] Find its angular acceleration when the stick is just released from the horizontal position in problem 2.
(b) [extra credit] What is the height of the static satellite of the earth?
(20 points)