Phy 121 - Assignment 11
A. vAAA = vBAB (Equation of continuity.)
(6.30 cm2)vA = (3.00 cm2)vB
2.10vA = vB
PA + ½ vA² +  ghA = PB + ½ vB² +  ghB (Bernoulli’s equation)
3.1 x 105 + ½(1000)vA² + 0 = 2.3 x 105 + ½(1000)vB² + (1000)(9.8)(6.5 m)
3.1 x 105 + 500vA² = 2.3 x 105 + 500vB² + .637 x 105
Substitute in 2.10vA = vB:
.163 x 105 + 500vA² = 500(2.10vA)²
.163 x 105 + 500vA² = 2205vA²
.163 x 105 = 1705vA²
9.56 = vA²
vA = 3.09 m/s (ans)
vB = 2.10vA = 6.49 m/s (ans)
B. 1. The level falls. While in the boat, the anchor is supported by buoyancy, and so
it displaces its weight of water, by making the boat sit low. When you throw the
anchor out, the boat pops up, lowering the water level. Submerged in the lake, the
anchor still displaces some water, but just its volume of water. Its weight of water
takes up more space than the anchor itself does, because the anchor is denser than
water.
2.
C. 1. Freezes: 0°C, 273 K, 32°F. Boils: 100°C, 373 K, 212°F. You should know
Celsius and Fahrenheit. You can convert Celsius to Kelvin using the table of units in
the formula sheet.
2.
D. 1. Speeds: vA is slowest, vB and vC are the same. From the equation of continuity,
Av = constant, the speed goes up as the pipe’s cross section goes down. The pipe is
larger at point A and the same size at B and C.
Pressures: PC is lowest, then PB, and PA is highest. It follows from Bernoulli’s equation
that when speed goes up pressure goes down, all else being equal. So vA < vB means PA
> PB. It also follows from Bernoulli’s equation that pressure decreases with height, all
else being equal. So PB > PC because C is higher.
2. If the volumes are the same, the buoyant forces are the same. It depends on the
weight of the displaced water, not the weight of the object itself.
3.
E.
F. 1. The temperatures must be in Kelvin not Celsius.
2. The first step is the free-body diagram. The
equations come from the picture, so if you can’t
draw the picture, you won’t be able to write the
equations.
∑Fy = 0
n – 33.95 = 0
n = 33.95 N
∑Fx = 0 (because the speed is constant, ax is zero.)
30 – f – 19.6 = 0
f = 10.4 N
f = μkn  μk
= .306