Chapter 7: Q21Q (page 170)
Why do you tend to lean backward when carrying a heavy load in your arms?
When you lean backward with a load in your arms, the center of mass becomes stable, and you are able to move forward without much difficulty.
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A 52-kg woman and a 72-kg man stand 10.0 m apart on nearly frictionless ice.
(a) How far from the woman is their CM?
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?
(c) How far will the man have moved when he collides with the woman?
The masses of the Earth and Moon are \({\bf{5}}{\bf{.98 \times 1}}{{\bf{0}}^{{\bf{24}}}}\;{\bf{kg}}\) and \({\bf{7}}{\bf{.35 \times 1}}{{\bf{0}}^{{\bf{22}}}}\;{\bf{kg}}\), respectively, and their centers are separated by \({\bf{3}}{\bf{.84 \times 1}}{{\bf{0}}^{\bf{8}}}\;{\bf{m}}\).
(a) Where is the CM of the Earth–Moon system located?
(b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?
A 0.145-kg baseball pitched horizontally at 27.0 m/s strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact.
A bullet of mass \(m{\bf{ = 0}}{\bf{.0010}}\;{\bf{kg}}\) embeds itself in a wooden block with mass \(M{\bf{ = 0}}{\bf{.999}}\;{\bf{kg}}\), which then compresses a spring \(\left( {k{\bf{ = 140}}\;{\bf{N/m}}} \right)\) by a distance \(x{\bf{ = 0}}{\bf{.050}}\;{\bf{m}}\) before coming to rest. The coefficient of kinetic friction between the block and table is \(\mu {\bf{ = 0}}{\bf{.50}}\).
(a) What is the initial velocity (assumed horizontal) of the bullet?
(b) What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?
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