[SOLVED] Physics 230 Homework Set 1

CQ1. Imagine holding two objects, a balloon and a rock, under water. Each object is precisely
equal in size.a) How do the buoyant forces, exerted on each of these two objects, compare?b) How do the buoyant forces compare when the balloon becomes deflated to half of
its original size?c) Now both objects of equal size are released from rest under water. Which object
floats and which object sinks? Why is this the case?CQ2. Water and oil do not mix and will stay separated when gently combined within a
container; it is noted that the density of oil is smaller than the density of water.
Imagine water being poured into a U-shaped tube that is open at both ends until the
water surface is halfway up each leg of the tube. Oil is then poured on top of the water
in the right leg only. Allowing the system to come to equilibrium, are the top of the
oil column in the right leg and the top of the water in the left leg at the same height?
If not, which is higher?CQ3. While driving your car, the passenger in the front seat lights a cigarette and opens the
window slightly. Why is it that the smoke blow out of the car? Why doesnt some of
the air from the outside flow into the car instead?P1. Consider your text book lying on a rock at sea level with the front cover facing up.
Your text is 7.0 mm thick, 21 cm wide, and 27 cm long with a mass of 320 g.
a) What is the average density of your favorite text book?b) How does the force exerted by atmospheric pressure on the front cover compare
with the force of gravity on the book? Express the answer as a ratio.P2. The earth has a mass of ME = 5.97 1024 kg and a radius of RE = 6.38 106 m.
Approximating the earth as a perfect sphere, calculate the average density of earth.P3. Boards used in building construction can typically withstand a pressure of 1.4 107 Pa
before being crushed. Assume that the mass density of these boards is 960 kg/m3.
Calculate the height, h, that these boards can be stacked before the boards at the
bottom of the pile are crushed. Assume that these boards are all identical and are
stacked precisely on top of one another.P4. Consider a hydraulic lift where you are standing on the left piston and a car is sitting on
the right piston. The pistons are at the same height above the ground and neither you
nor the car is moving. The piston on the right has a radius of 1.5 m. If the car has a
mass of 1200 kg and you have a mass of 65 kg, calculate the radius of the left piston.P5. You wish to calculate the lifting force of a helium balloon. You tie a long cord to the
balloon before releasing it and find that the balloon floats upward until it supports
8.46 cm of cord, where it then comes to equilibrium and hovers at a fixed height.A 100.-m length of the cord has a mass of 1.85 kg and the mass of the balloon, void of
helium, is 4.55 g. The mass densities of air and helium are 1.29 kg/m3 and 0.179 kg/m3,
respectively.a) Construct the free-body diagram for the balloon with a labeled force vector for
each individual force acting on the balloon.b) Calculate the volume of the inflated balloon?