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Physics 192 Practice Final Exam
The following is a practice exam designed to prepare you for the final.
The test is designed for practice rather than a representation of a typical
exam. It would therefore require somewhat more than 3 hours to work
through every problem thoroughly and thus should not be taken as an
example of typical exam length. Most of the course topics are covered
although this is not an exhaustive list.
Physics 192
Practice Final Exam
1. Find the impulse and the average force for applied forces and the time intervals
below:
a)
b)
Force vs. time
Force vs. time
120
F iˆ
(N)
120
80
F iˆ
(N)
40
200
400
t (ms)
600
800
80
40
200
400
600
t (ms)
2. A driver is sitting at a stoplight when suddenly her car is struck from behind by
another car. She is accelerated to a speed of 5.0 m/s in 0.29s. If her mass is 62 kg find
(a) the impulse on the driver and (b) the average force exerted on her by her car seat.
3. On an air track two gliders, one with a mass of 500 g and the other with a mass of
300 g, travel towards each other with speeds of 34 cm/s and 28 cm/s respectively.
When they collide the first bounces back with a speed of 12 cm/s. Find the final
speed of the second.
4. Two disks having the same density and thickness but different radii spin in opposite
directions with the same speed. When the smaller disk is suddenly coupled to the
larger disk, spinning freely at ωi , the angular velocity of the larger is reduced to
½ ωi ( the final velocity for both). Determine the ratio of their diameters.
800
5. A 3.25 kg mass on a frictionless surface is placed in front of a 585 N/m spring. When
the spring is compressed and released the mass is fired horizontally.
a) Calculate the distance by which the spring must be compressed so that the mass
has a maximum horizontal velocity of 75 cm/s.
b) Calculate the force required to hold the spring and the maximum acceleration of
the mass when released.
c) If the spring were now cut into two equal segments and placed sided by side
recalculate your answer for part a.
6. A 500 g mass oscillates with an 8 cm amplitude on the end of a 100 N/cm spring.
Find:
a) the period of oscillation
b) the displacement, velocity and acceleration 7 ms and 14 ms after leaving the
equilibrium position.
7. An 80 g mass attached to a 125 N/m spring is displaced 15 cm and released. Find:
a) the maximum velocity of the mass
b) the displacement at which the kinetic energy of the mass is equal to the potential
energy stored in the spring.
8. A 725 g pendulum swings with a period of 2.4 s and an amplitude of 18°.
a) Find the maximum velocity of the pendulum bob.
b) Find the displacement when the velocity is two thirds of this value.
9. A traveling wave is described by the equation:
s = (45 mm) sin 3/m[x - (15 m/s)t]
Determine:
a) the speed and wavelength and period of the wave
b) the amplitude, frequency of oscillation, and maximum velocity of the particle
vibrations as the wave passes a point in the medium.
10. A horizontal string is stretched over two pulleys with two 3.2 kg masses:
The equation of a transverse wave traveling in the string is:
S = (8.00 mm) sin [(15 m-1)(x – (85 m/s)t)]
a) Find the mass per unit length of the string
b) Find the frequency and maximum displacement of the oscillating particles.
11. A 256 Hz sound wave in travels in air at a temperature of –5 °C. Speed = 328m/s. The amplitude of
the oscillating particles is 2.2 mm.
a) Write the equation for this wave and the equation for the SHM of a particle at a
distance of 1.25 m along the path of the wave.
b) Calculate the maximum speed of the particle.
12. A 5.5 m long rope is fixed at both ends. The 2nd harmonic vibrates with a frequency
of 3.25 Hz when the tension is 40 N.
a) Determine the mass of the rope.
b) How long does it take for each of the component waves (the two interfering
waves travelling in opposite directions) to travel the length of the rope?
13. A 0.65 m long guitar string (E string) resonates with a fundamental frequency
of 165 Hz.
a) How far along the string must a finger be placed (in order to shorten the effective
length of the string) to produce a frequency of 196 Hz (G)
b) Remembering that a plucked guitar string entertains several harmonics
simultaneously, what is the lowest frequency heard when a finger just touches the
E string at 1/3 of the distance from the end?
14. A 20g ball moving at 5.00m/s strikes a stationary 30g ball. After the collision, the first ball moves
at 4.8m/s at an angle of 35 degrees with respect to the original line of motion. Find the struck balls'
velocity after the collision.
15. The concrete sections of a highway are 25.0 m long separated by 1.2 cm expansion
gaps at 15 °C. What is the maximum temperature which can be accommodated
before buckling?
16. At 20 °C, a copper ring has a radius of 5.000 cm while a steel sphere has a radius of
5.004 cm. Both expand as the temperature is increased. At what temperature will the
sphere slide easily through the ring?
17. How much water is boiled away when 500 g of aluminum at 450 °C is dropped into
0.75 L of water in a 100 g copper calorimeter cup, both at 80 °C ?
18. Find the total electric force on an electron placed at x=1.0m if 3nC is at x=0, -2nC
is at x=2.0m and -4nC is at x=4.0m.
.
19. Consider a charge q placed at a point 175 cm from a 5 µC charge. How far and in
what direction should one move q in order to reduce the electrostatic force by a factor
of 3?
20. Given the system of charges in the diagram below, find:
a) the total electric field strength at point A
b) the electric force which an electron would experience at point A.
Q =8.00 nC
1
3.00 cm
4.00 cm
A
B
.
6.00 cm
Q = -12.0 nC
2
21. For the two charges below
5 nC
-3 nC
50 cm
find the point where the electric field is zero.
22. For the circuit below, calculate the total resistance. Calculate the current, voltage,
and power for the 3300 Ω component.
250 Ω
1200 Ω
25 V
1800 Ω
250 Ω
3300 Ω
Answers:
1. a) 26 N⋅s iˆ , 32.5 N iˆ
b) 20 N⋅s iˆ , 25 N iˆ
2. (a) 310 N.s (b) 1069 N
3. 48.6 cm/s
4. Rsmaller/Rlarger = 0.76
5. a) 5.59 cm
b) 32.7 N, 10.1 m/s2
c) 2.8 cm
6. a) 44.4 ms
b) 6.7 cm, 6.2 m/s, -1340 m/s2 at 7 ms
7.3 cm, -4.5 m/s, -1470 m/s2 at 14 ms
7. a) 5.93 m/s
b) 10.6 cm
8. a) 1.17 m/s
b) 13.4°
9. a) 15 m/s, 2.09 m, 0.14 s
b) 45 mm, 7.16 Hz, 2.02 m/s
10. a) 4.3 g/m
b) 203 Hz, 8 mm
11. a) s = ( 2.2 mm ) sin ⎡⎣ 4.9 / m ( x − ( 328 m / s ) t ) ⎤⎦
or
⎡
⎛
⎞⎤
x
s = ( 2.2 mm ) sin ⎢1608 rad / s ⎜
− t ⎟⎥
⎝ 328 m / s ⎠ ⎦
⎣
b) 3.54 m/s
12. a) 0.689 Kg
b) 308 ms
13. a) 10.3 cm
b) 495 Hz (3rd harmonic)
14. 2.0 m/s at 69 degrees below horizontal
15. 55 °C
16. 180 °C
17. 41.6 g
18. 7.84 x 10-18 N left
19. 128 cm away
20. a) E = 8.54 x 104 N/C at -69.4°
b) 1.37 x 10-14 N at 110.6°
21. 1.72 m to the right of the -3nC charge
22. RT = 2071 Ω, IT = 12.1 mA, V3300 = 18.95 V, I3300 = 5.7 mA, P3300 = 108 mW