Download PH201-1E Final Comprehensive Exam (Apr. 30, 2007)

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PH201-1E Final Comprehensive Exam (Apr. 30, 2007)
• Write your name on the back side of the last page.
• There are 7 pages including this cover page. Check if you have all.
• You may not open the textbook nor notebook.
• A letter size information sheet may be used. Only mathematical formula, laws of physics,
physical principles can be written on the sheet. Solutions to homework problems, example
problems in the textbook, or any other problems explained classroom are not allowed in the
sheet.
• A letter size information may be used.
• A calculator may be used. However, mathematics or physics formula programmed in a calculator may not be used.
• Write down, reasoning, calculation and answer in the blank space after each problem. Use
the backside of the sheet if necessary.
• Answers without reasonable explanation nor mathematical derivation will receive
no point even if your final answer coincides with the correct one. Explanation
must begins with basic principles.
• Don’t forget units in the final answers!
[a]
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1. [ 30 pts. (5 pts. each)] Multiple choice problems: Choose one from the selection that is the
closest to your answer. (No explanation is required for the multiple choice problems.)
1.1. Starting from rest, a speedboat reaches a speed of 3.2 m/s in 1.6 s. What is the boat’s speed
after an additional 2.4 s has elapsed, assuming the boat’s acceleration remains the same?
(a) 8.0 m/s
(b) 9.0 m/s
(c) 10 m/
(d) 11 m/s
1.2 Two forces, F1 and F2 , act on the m = 5.0 kg block shown in
Figure. The magnitudes of the forces are F1 = 22 N and F2 = 26 N .
The direction of F1 is θ= 60◦ . What is the horizontal acceleration of
the block? (To the right is positive.)
(a) −3.0 m/s2
(d) +1.0 m/s2
(b) −2.0 m/s2
(e) +2.0 m/s2
(c) −1.0 m/s2
(f) +3.0 m/s2
1.3 Figure shows a boat being pulled by two locomotives through
a canal of length 3.2 km. The tension in each cable is 6.0 × 103 N ,
and θ=20◦ . What is the net work done on the boat by the two
locomotives?
(a) 1.3 × 104 kJ
(d) 4.3 × 104 kJ
(b) 2.1 × 104 kJ
(e) 5.6 × 104 kJ
(c) 3.6 × 104 kJ
(f) 6.8 × 104 kJ
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(e) 12 m/s
1.4 Kevin has a mass of 85 kg and is skating with in-line skates. He sees his 21-kg younger
brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he
grabs his brother and rolls off at a speed of 2.2 m/s. Ignoring friction, find Kevin’s speed just
before he grabbed his brother.
(a) 2.2 m/s
(b) 2.5 m/s
(c) 2.7 m/s
(d) 3.0 m/s
(e) 3.2 m/s
(f) 3.5 m/s
1.5 You are installing a new spark plug in your car, and the manual
specifies that it be tightened to a torque that has a magnitude of 40
N ·m. Using a wrench of length L=0.27 m at angle θ=55◦ , determine
the magnitude of the force F that you must exert on the wrench.
(a) 1.5 × 102 N
(d) 2.4 × 102 N
(b) 1.8 × 102 N
(e) 2.7 × 102 N
(c) 2.1 × 102 N
(f) 3.0 × 102 N
1.6 A simple pendulum is made from a 0.44 m-long string and a small ball attached to its free
end. The ball is pulled to one side through a small angle and then released from rest. After the
ball is released, how much time elapses before it attains its greatest speed?
(a) 0.33 s
(b) 0.37 s
(c) 0.40 s
(d) 0.46 s
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(e) 0.51 s
(f) 0.55 s
2.[15 pts] A baseball player hits a ball and
the ball leaves the bat with an initial velocity
32 m/s at an angle 35◦ above the horizontal.
The ball flies toward the left-field seats 95 m
from the player. However, there is 6-m high
fence in front of the seats (see Figure). Assume that the ball is 1 m above the ground
when it is hit by the bat. Ignore air resistance. You must derive final results from the
basic kinematic equations.
(a) Find the maximum height that the ball attains.
(b) How long does it take for the ball to reach the highest position?
(c) Determine if it is a home run (Determine if the ball flies over the fence). [Don’t forget that
the ball was initially 1 m above the ground.]
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3. [15 pts.] A 12-kg uniform board is wedged into a corner
and held by a spring at a 55◦ angle as shown in Figure.
The length of the board is 40 cm. The spring has a spring
constant of 150 N/m and is parallel to the floor.
(a) Choosing an axis of rotation at the wedge. what is
the torque due to the weight?
(b) Find the amount by which the spring is stretched
from its unstrained length.
(c) Find the magnitude of the force exerted on the board
by the corner at the wedge.
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4. [20 pts.] An end of a 0.64-m string is attached to a
vertical rod and the other end to a 0.45-kg ball as shown
in Figure. When the rod spins, the ball is whirled around
in a horizontal circle. The angle between the rod and the
string is 60◦ .
(a) What is the magnitude of the tension in the string?
(b) What is the magnitude of the centripetal force?
(c) What is the tangential speed of the ball?
(d) What is the angular speed of the ball?
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5. [20 pts.] A block of mass m=39 kg is sliding on a
30◦ incline (see Figure.) It starts from rest at the top
of the incline 10 m above the baseline and reaches
the bottom of the incline. The coefficient of kinetic
friction between the block and incline is µk =0.26.
Ignore the size of the block and air resistance.
(a) Find the frictional force exerted on the block.
(b) Find the work done on block by the frictional
force.
(c) Find the acceleration of the block.
(d) Find the kinetic energy of the block when it
reaches the bottom.
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