Chapter 1: Mechanics

You are captured by Martians, taken into their ship, and put to sleep. You awake some time later and find yourself locked in a small room with no windows. All the Martians have left you with is your digital watch, your school ring, and your long silverchain necklace. Explain how you can determine whether you are still on earth or have been transported to Mars

A valued client brings a treasured ball to your engineering firm, wanting to know whether the ball is solid or hollow. He has tried tapping on it, but that has given insufficient information. Design a simple, inexpensive experiment that you could perform quickly, without injuring the precious ball, to find out whether it is solid or hollow.

Some people say that the “force of inertia” (or “force of momentum”) throws the passengers forward when a car brakes sharply. What is wrong with this explanation?

In Example 8.7 (Section 8.3), where the two gliders ofFig. 8.18 stick together after the collision, the collision is inelastic because${\mathit{K}}_{\mathbf{1}}\mathbf{<}{\mathit{K}}_{\mathbf{2}}$ . In Example 8.5 (Section 8.2), is the collisioninelastic? Explain

If a jumping frog can give itself the same initial speed regardless of the direction in which it jumps (forward or straight up), how is the maximum vertical height to which it can jump related to its maximum horizontal range ${\mathit{R}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{=}\frac{{\mathbf{v}}_{\mathbf{0}}^{\mathbf{2}}}{\mathbf{g}}$?

For the cases shown in Fig. Q6.8, the object is released from rest at the top and feels no friction or air resistance. In which (if any) cases will the mass have (i) the greatest speed at the bottom and (ii) the most work done on it by the time it reaches the bottom?

You drop a solid sphere of aluminium in a bucket of water that sits on the ground. The buoyant force equals the weight of water displaced; this is less than the weight of the sphere, so the sphere sinks to the bottom. If you take the bucket with you on an elevator that accelerates upward, the apparent weight of the water increases and the buoyant force on the sphere increases. Could the acceleration of the elevator be great enough to make the sphere pop up out of the water? Explain.

A planet makes a circular orbit with period Taround a star. If the planet were to orbit at the same distance around this star, but the planet had three times as much mass, what would the new period (in terms of T) be: (a) 3T, (b) $\mathbf{T}\sqrt{\mathbf{3}}$, (c) $\mathit{T}\mathit{l}\sqrt{\mathbf{3}}$ (d), or (e) T/3?

You drop a solid sphere of aluminium in a bucket of water that sits on the ground. The buoyant force equals the weight of water displaced; this is less than the weight of the sphere, so the sphere sinks to the bottom. If you take the bucket with you on an elevator that accelerates upward, the apparent weight of the water increases and the buoyant force on the sphere increases. Could the acceleration of the elevator be great enough to make the sphere pop up out of the water? Explain.

You walk into an elevator, step onto a scale, and push the “up” button. You recall that your normal weight is 625 N. Draw a free-body diagram.

(a) When the elevator has an upward acceleration of magnitude$2.5m/S^2$, what does the scale read?

(b) If you hold a 3.85 kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)?