PHYS1224 – FALL 2006
EXAM 1 – PART 2
TUESDAY’S VERSION
NAME: ___________________________________________________
1.
______________________________
(20 pts)
2.
______________________________
(25 pts)
3.
______________________________
(35 pts)
4.
______________________________
(30 pts)
5.
______________________________
(30 pts)
6.
______________________________
(15 pts)
7.
______________________________
(10 pts)
8.
______________________________
(20 pts)
9.
______________________________
(10 pts)
10.
______________________________
(16 pts)
11.
______________________________
(15 pts)
12.
______________________________
(14 pts)
Total Part II _________________________
(240 pts)
1. A 2500 kg race car is traveling around a flat circular race trace of radius 230m.
What is the minimum coefficient of static friction required between the tires and the
race track if the car is to stay on the track at a speed of 130 m/s?
r
2.
You are given the following vectors:


A   5m î  2m ĵ , B   3m î  7m ĵ ,

D   3m î  4m ĵ  5m k̂

C  4m 285 ,
A.

What is the magnitude and direction of vector A ?
B.

Write C in Cartesian form?
C.
 

What is E  2A  B in Cartesian form?
D.
 
Determine A  B
E.
 
Write vector D  B in Cartesian form.
3.
Two blocks of mass 3.50 kg and 8.00 kg are connected by a string that passes
over a frictionless pulley of negligible mass as shown below. The inclinations are
frictionless.
8 kg
3.5 kg
25
40
A.
Draw and label free body diagrams for both masses
B.
Find the acceleration of the 8.00 kg block
C.
Find the tension in the string.
D.
Assume that the blocks are initially at rest. What is the displacement of the 8.00
kg block, four seconds after the blocks are released.
4.
A 6.00-kg block is placed on top of a 8.0-kg block as shown below. A horizontal
force of 65.0 N is applied to the 8.0-kg block, and the 6.00-kg block is tied to the
wall using a string of negligible mass. The coefficient of kinetic friction between
all surfaces is 0.250.
6kg
8 kg
A.
Draw the free-body diagram for each block.
F
B.
Determine the acceleration of the 8.0-kg block.
C.
Determine the tension in the string.
5.
A placekicker must kick a football from a point 36.0 m (about 40 yards) from the
goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m
high. When kicked, the ball leaves the ground with a speed of 27.0 m/s at an angle
of 48.0° to the horizontal.
48
SCRATCH AREA FOR SETTING UP THE PROBLEM
A)
What is the football’s initial velocity in the x-direction?
B)
What is the football’s initial velocity in the y-direction?
C)
By how much does the football clear or fall short of clearing the crossbar?
D)
Does the football approach the crossbar while still rising or while falling? (Justify
your answer with a calculation)
6.
A ball’s position-time graph is shown below,
x (m)
12
8
4
t (s)
2
4
6
8
10
determine
A.
the displacement of the ball from t = 2 s to t = 10 s.
B.
the velocity of the ball at t = 8s.
C.
the position of the ball at t = 8s?
7.
A person is at an amusement park riding inside the barrel of fun of radius R. The
person is standing against the wall of the ride with a coefficient of static friction
 s between the person and the wall of the ride. The operator starts the barrel
spinning and increases the barrel’s speed. Once the rider is traveling at a
sufficiently large tangential speed v, the operator is planning to drop the floor
from the ride. Show that the rider must be traveling at a speed of at least
gR
in order not to fall when the floor is removed.
v
s
R
8.
The velocity of a particle that is initially located at the origin is given by

3
v  {(t  3t  6)î  (-2t  5)ĵ } m/s
A.
What is the velocity of the particle at t = 2s ?
B.
What is the acceleration of the particle at t = 2s?
C.
What is the position of the particle at t = 2s?
D.
What is the average velocity of the particle over the time interval t = 0s to t = 3s?
9.
The space shuttle makes a landing at Kennedy Space Center (KSC) with a speed
of 320 m/s. Assuming that the KSC runway is 410 m in length, what is the
minimum average acceleration required to bring the shuttle to rest without
crashing.
10.
A.
Short Answer (4 pts each)
A simple pendulum (a mass swinging at the end of a string) swings back and for in a
circular arc. What is the direction of its acceleration at the ends of the swing? At the
midpoint? In each case explain how you obtain your answer.
B. A woman in an elevator lets go of her briefcase but it does not fall to the floor.
Describe how the elevator is moving?
C.
Suppose you are driving a car along a highway at a high speed. Using Leonardo’s
de Vici’s Laws of Sliding friction, explain why you should avoid slamming on the
brakes in order to stop in the shortest distance possible.
D.
In the motion picture It Happened One Night, Clark Gable is standing inside a
stationary bus in front of Claudette Colbert, who is seated. The bus suddenly
starts moving forward, and Clark falls into Claudette’s lap. Why did this happen?
11.
In lab you drop a ball from a height above the floor and then measure the
maximum height which the ball obtains following each successive bounce. The
data from the experiment is provided in the table below. Graphically determine
the mathematical equation relating the maximum bounce height to the number of
bounces using the log-log, semi-log, and linear graph paper provided. All
calculations and graphs must be provided for credit. The axis on your graphs must
be labeled. No credit will be given for calculator solutions or guessing.
Bounce
1
2
3
4
Height (centimeters)
200. +/- 2
51 +/- 2
23 +/- 1
12.0 +/- 0.5
Bounce
5
6
7
8
Height (centimeters)
8.2 +/- 0.3
5.6 +/- 0.3
4.2 +/- 0.3
3.0 +/- 0.3
12.
A TSU student repeatedly measures the time that it takes for a pendulum to
complete a single cycle. The times measured by the statement are given below:
Trial #
1
2
3
4
5
6
Time (s)
22.37
24.56
20.37
26.45
18.97
20.04
A.
What is the average time for the pendulum to complete one cycle?
B.
What is the absolute uncertainty for the time?