Chapter 1: Mechanics

Friends Burt and Ernie stand at opposite ends of a uniform log that is floating in a lake. The log is 3.0 m long and has mass 20.0 kg. Burt has mass 30.0 kg ; Ernie has mass 40.0 kg. Initially, the log and the two friends are at rest relative to the shore. Burt offers Ernie a cookie, and Ernie walks to Burt’s end of the log to get it. Relative to the shore, what distance has the log moved by the time Ernie reaches Burt? Ignore any horizontal force that the water exerts on the log , and assume that neither friends falls off the log.

The human circulatory system is closed—that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart’s four chambers comes briefly to rest before it is ejected by contraction of the heart muscle

If the aorta (diameter d_a) branches into two equal-sized arteries with a combined area equal to that of the aorta, what is the diameter of one of the branches? (a)$\sqrt{\mathbf{d}}$; (b)$\frac{\mathbf{d}}{\sqrt{\mathbf{2}}}$; (c)$\mathbf{2}\mathbf{d}$; (d)role="math" localid="1655806881203" $\frac{{\mathbf{d}}_{\mathbf{a}}}{\mathbf{2}}$

How does the force the diaphragm experiences due to the difference in pressure between the lungs and abdomen depend on the abdomen’s distance below the water surface? The force (a) increases linearly with distance; (b) increases as distance squared; (c) increases as distance cubed; (d) increases exponentially with distance.

Question: When an object is rolling without slipping, the rolling friction force is much less than the friction force when the object is sliding; a silver dollar will roll on its edge much farther than it will slide on its flat side (see Section 5.3). When an object is rolling without slipping on a horizontal surface, we can approximate the friction force to be zero, so that \({a_x}\) and \({a_z}\) are approximately zero and \({v_x}\) and\({\omega _z}\) are approximately constant. Rolling without slipping means\({v_x} = r{\omega _z}\;{\rm{and}}\;{a_x} = r{\alpha _z}\). If an object is set in motion on a surface withoutthese equalities, sliding (kinetic) friction will act on the object as it slips until rolling without slipping is established. A solid cylinder with mass M and radius R, rotating with angular speed \({\omega _0}\) about an axis through its center, is set on a horizontal surface for which the kinetic friction coefficient is \({\mu _k}\). (a) Draw a free-body diagram for the cylinder on the surface. Think carefully about the direction of the kinetic friction force on the cylinder. Calculate the accelerations \({a_x}\) of the center of mass and \({a_z}\) of rotation about the center of mass. (b) The cylinder is initially slipping completely, so initially \({\omega _z} = {\omega _0}\) but \({v_x} = 0\). Rolling without slipping sets in when \({v_x} = r{\omega _z}\). Calculate the distance the cylinder rolls before slipping stops. (c) Calculate the work done by the friction force on the cylinder as it moves from where it was set down to where it begins to roll without slipping.

The Effective Force Constant of Two Springs. Two springs with the same unstretched length but different force constants \({k_1}\) and \({k_2}\) are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant \({k_{eff}}\) in each of the three cases (a), (b), and (c) depicted in Fig. P14.92. (The effective force constant is defined by \(\sum {F_x} = - {k_{eff}}x\) ) (d) An object with mass m, suspended from a uniform spring with a force constant k, vibrates with a frequency \({f_1}\). When the spring is cut in half and the same object is suspended from one of the halves, the frequency is \({f_2}\). What is the ratio \({f_1}/{f_2}\)?

For a physics lab experiment, four classmates run up the stairs from the basement to the top floor of their physics building—a vertical distance of16.0 m. The classmates and their masses are: Tatiana,50.2 kg; Bill,68.2 kg; Ricardo,81.8 kg; and Melanie,59.1 kg. The time it takes each of them is shown in Fig. P6.92. (a) considering only the work done against gravity, which person had the largest average power output? The smallest? (b) Chang is very fit and has mass62.3 kg. If his average power output is 1.00 hp, how many seconds does it take him to run up the stairs?

A 45.0-kg woman stands up in a 60.0-kg canoe 5.00 m long. Se walks from a point 1.00 m from one end to a point 1.00 m from the other end (Fig. P8.92). If you ignore resistance to motion of the canoe in water, how far does the canoe move during this process?

Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop (Fig. P5.92). There is no friction between block Aand the tabletop, but the coefficient of static friction between blocks Aand Bis 0.750. A light string attached to block Apasses over a frictionless, massless pulley, and block Cis suspended from the other end of the string. What is the largest mass that block Ccan have so that blocks Aand Bstill slide together when the system is released from rest?

If the elephant were to snorkel in salt water, which is denser than freshwater, would the maximum depth at which it could snorkel be different from that in freshwater? (a) Yes—that depth would increase, because the pressure would be lower at a given depth in salt water than in freshwater; (b) yes—that depth would decrease, because the pressure would be higher at a given depth in salt water than in freshwater; (c) no, because pressure differences within the submerged elephant depend on only the density of air, not the density of the water; (d) no, because the buoyant force on the elephant would be the same in both cases.

American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders1.0mlong and 10cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. Eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. Although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could

A field researcher uses the slow-motion feature on her phone’s camera to shoot a video of an eel spinning at its maximum rate. The camera records at 120 frames per second. Through what angle does the eel rotate from one frame to the next?

1. ${\mathbf{1}}^{\mathbf{\circ }}$
   
2. ${\mathbf{10}}^{\mathbf{\circ }}$
   
3. ${\mathbf{22}}^{\mathbf{\circ }}$
   
4. ${\mathbf{42}}^{\mathbf{\circ }}$