Physics 207w, w2 (Summer) Exam 1

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

June 25, 1998
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ Recitation Section: ______________________________________________________________________________________________

General Instruction

You have 1 hour to answer 4 questions 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.

Take the following in the exam:

2 g = 10m/s sin 37o = 0.6 o cos64 = 0.8

1. A rectangle block 0.12m high and 0.06m wide is made up of two uniform sub-blocks of same size 0.06m × 0.06m × 0.06m. The upper sub-block weighs 16N and the lower sub-block weighs 8N. If this rectangle block is dragged to the right along a level surface at constant speed by a horizontal force P , as shown in the figure below. The coefficient of sliding friction is 0.50,
(a) Where is the gravity center of the rectangle block? Draw the coordinate system on the figure below.
(b) Find the magnitude of the force P .
(c) If h = 0.04m, find the position of the line of action of the normal force N exerted on the block by the surface.
(d) Draw the free body diagram for (c) on the figure below.
(e) Find the value of h at which the block just starts to tip.
(30 points)

2. A ladder of mass M = 25kg rests against a frictionless wall as shown in the figure below. The length of the ladder is l, and the angle between the ladder and the ground is h = 60o.
(a) Draw the free body diagram for the ladder.
(b) Find the force on the ladder exerted by the wall using the second condition of equilibrium. Which point should be chosen to calculate the torques here?
(c) Find the forces on the ladder exerted by the ground.
(d) If the ladder stands without slipping, what is minimum coefficient of friction between ladder and the ground?
(30 points)

3. A rifle bullet is fired with a speed of 100m/s at a small target on the same level and 300m away. Neglect the friction of the air.
(a) At what angle h above the horizontal must the bullet be fired to hit the target? It may be helpful to recall that sin 2h = 2 sin h cos h.
(b) How long is the time bullet in flight?
(c) What is the maximum height of the bullet?
(20 points)

4. The apparent weight w' of an object is the upward force exerted by its supporting surface. A passenger in a Ferris wheel rotates 3 revolutions/min in a vertical circle of radius 5m,
(a) Find the central-petal acceleration at the top and the bottom of the circle, indicating its direction.
(b) Find the ratio of his apparent weight to his true weight at the top and the bottom of the circle.
(20 points)