Chapter 1: Mechanics

Power of the Human Heart. The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7500 L of blood. Assume that the work done by the heart is equal to the work required to lift this amount of blood a height equal to that of the average American woman (1.63 m). The density (mass per unit volume) of blood is$\mathbf{1}\mathbf{.}\mathbf{05}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathit{k}\mathit{g}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$. (a) How much work does the heart do in a day? (b) What is the heart’s power output in watts?

A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component \({v_x}\) as a function of time t. Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in cm), and at what times does the mass reach this position? (e) Find the maximum acceleration magnitude of the mass and the times at which it occurs. (f) What is the value of m?

Block Ain Fig. P5.89 has mass 4.00 kg, and block Bhas mass 12.00 kg. The coefficient of kinetic friction between block B and the horizontal surface is 0.25. (a) What is the mass of block C if block Bis moving to the right and speeding up with an acceleration of $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$? (b) What is the tension in each cord when block B has this acceleration?

Question:Block Ain Fig. P5.89 has mass , and block Bhas mass . The coefficient of kinetic friction between block B and the horizontal surface is . (a) What is the mass of block C if block Bis moving to the right and speeding up with an acceleration of ? (b) What is the tension in each cord when block B has this acceleration?

For the situation shown, the tissues in the elephant’s abdomen are at a gauge pressure of 150 mm Hg. This pressure corresponds to what distance below the surface of a lake? (a) 1.5 m;(b) 2.0 m; (c) 3.0 m; (d) 15 m.

You are designing a flywheel to store kinetic energy. If all of the following uniform objects have the same mass and same angular velocity, which one will store the greatest amount of kinetic energy? Which will store the least? Explain. (a) A solid sphere of diameter D rotating about a diameter; (b) a solid cylinder of diameter D rotating about an axis perpendicular to each face through its center; (c) a thin-walled hollow cylinder of diameter D rotating about an axis perpendicular to the plane of the circular face at its center; (d) a solid, thin bar of length D rotating about an axis perpendicular to it at its center

A driver in Massachusetts was sent to traffic court for speeding. The evidence against the driver was that a policewoman observed the driver’s car alongside a second car at a certain moment, and the policewoman had already clocked the second car going faster than the speed limit. The driver argued, “The second car was passing me. I was not speeding.” The judge ruled against the driver because, in the judge’s words, “If two cars were side by side, both of you were speeding.” If you were a lawyer representing the accused driver, how would you argue this case?

A block rests on an inclined plane with enough friction to prevent it from sliding down. To start the block moving is it easier to push it up the plane or down the plane? Why?

Fractured Physics. People often call their electric bill a power bill, yet the quantity on which the bill is based is expressed in kilowatt-hours. What are people really being billed for?

8. You freely pivot a horseshoe from a horizontal nail through one of its nail holes. You then hang a long string with a weight at its bottom from the same nail, so that the string hangs vertically in front of the horseshoe without touching it. How do you know that the horseshoe’s center of gravity is along the line behind the string? How can you locate the center of gravity by repeating the process at another nail hole? Will the center of gravity be within the solid material of the horseshoe?