1 - University of California, San Diego



1. A pendulum clock is set to run accurately at sea level. It is then brought to the top of a high mountain, where it is found to (a) function unchanged (b) run slow (c) run fast (d) stop running (e) none of these.

2. A 5.0-g bullet is fired horizontally into a 0.50-kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-spring system goes into SHM with a frequency of 9.0 Hz and an amplitude of 15 cm. Determine the initial speed of the bullet.

3. A horizontal stretched string carries a sinusoidal wave described by the following equation:

y = 0.1 sin(2x + 3t)

a) In what direction along the x-axis is the wave moving?

b) What is the amplitude?

c) What is the wavelength of the wave?

d) Calculate the speed of a piece of string at x = 1m and t = 2 sec.

4. Why do you see lightning before you see thunder? A familiar rule is that if you start to count the seconds when you see the lightning flash, and stop when you hear the thunder, divide that number by five, that gives the distance to the flash in miles. Is this correct?

5. The following two graphs give snapshots of a wave pulse at t = 0 sec and t = 1 sec. What is the wave speed? Draw a history graph for x = 4m, and for x = 6m.

L

1. g is smaller on the top of a high mountain. With T = 2([pic], it follows T gets bigger. Pendulum clock runs slow. Therefore, (b) is the correct answer.

2. Energy is not conserved though momentum is;

mbvb = (mb + M)v0; v0 = 2(fx0 = 8.48 m/s;

(0.005 0 kg)vb = (0.505 kg) (8.48 m/s) and so vb = 0.86 km/s.

3. Compare y = 0.1 sin(2x + 3t) with y = 0.1 sin2([pic] for a wave in the negative x direction. So 2 = [pic] hence ( = ( m/sec and 3 = [pic] or T = [pic] = 2.09 sec. Hence, equation can be written as

y = A sin2([pic]

(a) Wave is moving in negative x direction, (coefft of x is positive)

(b) The amplitude is 0.1

(c) Wavelength ( = ( = 3.14 m

(d) Speed of particle = dy/dt. Differentiate y = 0.05 sin(2x + 3t).

[pic] = 3 x 0.05 cos(2x + 3t). Subs x = 1m and t = 2sec gives

[pic] = 0.15 cos(2+6) = 0.15 x (-0.15) = -0.02 m/sec

4. Light travels faster than sound, so light from the flash of lightning will reach an observer earlier than the sound from the thunder. Sound travels approx 750 mph, or about 12 miles per minute, or 1 mile in 5 seconds. Light travels at 3 x 108 m/s or 186,000 miles/sec, this is so fast that for this purpose we can ignore the light travel time. So there is a time lag of 5 sec for every mile of distance between observer and lightning flash. The rule is OK. (Note the flash may not be at ground level, does this matter?)

5. From the snapshots pulse moves 2 m in 1 sec, so speed is 2m/sec.

-----------------------

y

y

t = 0 sec

0 2 4 6

t = 1 sec

0 2 4 6

x(m)

x(m)

y

y

t

t

History graph for x = 4m

History graph for x = 6m

1 2 3

1 2 3

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