Homework Problems

1	An object is observed to be moving at constant speed in a certain direction. Can you conclude that no forces are acting on it? Explain. [Based on a problem by Serway and Faughn.]
2	A car is normally capable of an acceleration of 3 m/s2. If it is towing a trailer with half as much mass as the car itself, what acceleration can it achieve? [Based on a problem from PSSC Physics.]
3	(a) Let T be the maximum tension that the elevator's cable can withstand without breaking, i.e., the maximum force it can exert. If the motor is programmed to give the car an acceleration a, what is the maximum mass that the car can have, including passengers, if the cable is not to break? (b) Interpret the equation you derived in the special cases of a = 0 and of a downward acceleration of magnitude g. ("Interpret" means to analyze the behavior of the equation, and connect that to reality, as in the self-check on page 139.)	√
4	A helicopter of mass m is taking off vertically. The only forces acting on it are the earth's gravitational force and the force, Fair, of the air pushing up on the propeller blades. (a) If the helicopter lifts off at t = 0, what is its vertical speed at time t? (b) Plug numbers into your equation from part a, using m = 2300 kg, Fair = 27000 N, and t = 4.0 s.
5	In the 1964 Olympics in Tokyo, the best men's high jump was 2.18 m. Four years later in Mexico City, the gold medal in the same event was for a jump of 2.24 m. Because of Mexico City's altitude (2400 m), the acceleration of gravity there is lower than that in Tokyo by about 0.01 m/s2. Suppose a high-jumper has a mass of 72 kg. (a) Compare his mass and weight in the two locations. (b) Assume that he is able to jump with the same initial vertical velocity in both locations, and that all other conditions are the same except for gravity. How much higher should he be able to jump in Mexico City? (Actually, the reason for the big change between '64 and '68 was the introduction of the "Fosbury flop.") ?	√ *
6	A blimp is initially at rest, hovering, when at t = 0 the pilot turns on the motor of the propeller. The motor cannot instantly get the propeller going, but the propeller speeds up steadily. The steadily increasing force between the air and the propeller is given by the equation F = kt, where k is a constant. If the mass of the blimp is m, find its position as a function of time. (Assume that during the period of time you're dealing with, the blimp is not yet moving fast enough to cause a significant backward force due to air resistance.)	∫
7	car is accelerating forward along a straight road. If the force of the road on the car's wheels, pushing it forward, is a constant 3.0 kN, and the car's mass is 1000 kg, then how long will the car take to go from 20 m/s to 50 m/s?	Solution, p. 279
8	Some garden shears are like a pair of scissors: one sharp blade slices past another. In the "anvil" type, however, a sharp blade presses against a flat one rather than going past it. A gardening book says that for people who are not very physically strong, the anvil type can make it easier to cut tough branches, because it concentrates the force on one side. Evaluate this claim based on Newton's laws. [Hint: Consider the forces acting on the branch, and the motion of the branch.]
9	A uranium atom deep in the earth spits out an alpha particle. An alpha particle is a fragment of an atom. This alpha particle has initial speed v, and travels a distance d before stopping in the earth. (a) Find the force, F, that acted on the particle, in terms of v, d, and its mass, m. Don't plug in any numbers yet. Assume that the force was constant. (b) Show that your answer has the right units. (c) Discuss how your answer to part a depends on all three variables, and show that it makes sense. That is, for each variable, discuss what would happen to the result if you changed it while keeping the other two variables constant. Would a bigger value give a smaller result, or a bigger result? Once you've figured out this mathematical relationship, show that it makes sense physically. (d) Evaluate your result for m = 6.7×10-27 kg, v = 2.0×104 km/s, and d = 0.71 mm. p	√
10	You are given a large sealed box, and are not allowed to open it. Which of the following experiments measure its mass, and which measure its weight? (a) Put it on a frozen lake, throw a rock at it, and see how fast it scoots away after being hit. (b) Drop it from a third-floor balcony, and measure how loud the sound is when it hits the ground. (c) As shown in the figure, connect it with a spring to the wall, and watch it vibrate. [Hint: Which experiments would give different results on the moon?]
11	While escaping from the palace of the evil Martian emperor, Sally Spacehound jumps from a tower of height h down to the ground. Ordinarily the fall would be fatal, but she fires her blaster rifle straight down, producing an upward force FB. This force is insufficient to levitate her, but it does cancel out some of the force of gravity. During the time t that she is falling, Sally is unfortunately exposed to fire from the emperor's minions, and can't dodge their shots. Let m be her mass, and g the strength of gravity on Mars. (a) Find the time t in terms of the other variables. (b) For sufficiently large values of FB, your answer to part a becomes nonsense - explain what's going on.

Rockets work by pushing exhaust gases out the back. Newton's third law says that if the rocket exerts a backward force on the gases, the gases must make an equal forward force on the rocket. Rocket engines can function above the atmosphere, unlike propellers and jets, which work by pushing against the surrounding air.