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3. (36) In a physics experiment, an iron casting
with an empty cavity is completely
submerged in an open container of water.
The casting is suspended by a
cord connected to the ceiling of the laboratory. A schematic of the situation
is shown below. The tension in the cord is T = 4000 N. The mass M of the
casting is 600 kg. The density of iron
(that is, a sample with no cavities) is 7870 kg/m3 . The density
of water is assumed to exactly 1000 kg/m3.
(a) (4) What is the volume VD
of water displaced by the casting?
(b) (22)What is the volume VC of the empty cavity?
(c) (2) Suppose the cord breaks.
Immediately after the cord breaks, what direction does the casting move, up
or down? Circle one.
(d) (8) What is the magnitude | a |
of the acceleration while it moves ?
4. (25) A sealed tank contains pure distilled
water (of density = exactly
1000 kg/m3) to a height exactly
10.0 m above the level of a hole. ( y1 – y2 = 10.0
m.) Water exits the hole with an efflux speed v2. The water flows into a nearby container
that can hold 600.0 L of liquid when
full. In this scenario we assume the water level in the tank does not change since the speed v1 of the liquid surface is very small (i.e.
essentially zero). In the tank, the
absolute pressure in the air above the water is P1 = 4.00
atm. Assume the area of the hole is A2
= 0.0010 m2.
How long (in seconds) does it take for the 600.0 L container to be filled
up to the brim? (Note: 1 L = 1x10-3 m3 and 1 atm = 1.013x105 N/m2.)
5. (40) Two triangular waves are traveling toward each other on a
stretched string. Each pulse is identical and travels at speed 4.00
cm/s. The leading edges of the pulses just
touch at t = 0.
(a) (10) Sketch carefully the shape of the string at t = 0.625 seconds.
(b) (5) What is the total width of the
wave form at t = 0.625 seconds?
(c) (10) Sketch carefully the shape of the string at t = 1.25 seconds.
(d) (5) What is the total width of the
wave form at t = 1.25 seconds?
(e) (5) What is the maximum height of the wave form at t = 1.25 seconds?
(f) (5) Sketch
carefully the shape of the string at t = 2.5 seconds.
6.
(23) A thin taut string tied at both ends and oscillating
in its fourth harmonic has a shape
given by
y(x,t) = (8.40 cm) sin[(0.440π rad/m)x]sin[(50.0π rad/s)t].
The origin is at the left end of the string and the x- axis is along the
string. The y-axis is perpendicular to the string. Assume right is the
positive x-direction. Assume up is the positive y-direction.
(a) (2)What is the length L of the string?
(b) (2) Sketch the standing wave pattern between x = 0 and x = L, inclusive.
(c) (2)Find the amplitude A of each of the two traveling waves making up the
wave.
(d) (4)Find the maximum transverse
speed |vy| of a point on the string?
(e) (4) At what values of x does the maximum transverse speed occur?
(f) (4)At the position x = 3.0 cm and
time t = 0.06 sec, is a point on the string moving up or down? Show work.
(g) (3) What would be the equation y(x,t) if this string were vibrating in
the first harmonic ?
(h) (2) Sketch the standing wave pattern between x = 0 and x = L, inclusive,
for first harmonic.
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