91Ó°ÊÓ

Two masses$m_{\mathrm{A}}=2.0\mathrm{kg}$and$m_{\mathrm{B}}=5.0\mathrm{kg}$are on inclines and are connected together by a string as shown in Fig. 4–61. The coefficient of kinetic friction between each mass and its incline is${\mathrm{μ}}_{\mathrm{k}}=0.30$. If$m_{\mathrm{A}}$moves up, and$m_{\mathrm{B}}$moves down, determine their acceleration. [Ignore masses of the (frictionless) pulley and the cord.]

Question: A child slides down a slide with a${34}^{\mathrm{o}}$incline and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

Question: (a) Suppose the coefficient of kinetic friction between $m_A$and the plane in Fig. 4-62 is ${\mathrm{μ}}_k=0.15$and that $m_A=m_{\mathrm{B}}=2.7\mathrm{kg}$. As,$m_B$moves down, determine the magnitude of acceleration of$m_A$and$m_{\mathrm{B}}$, given$\mathrm{θ}={34}^{\mathrm{o}}$. (b) What smallest value of${\mathrm{μ}}_k$will keep the system from accelerating? [Ignore masses of the (frictionless) pulley and the cord.]

A 2.0 kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of $27\mathrm{m}/\mathrm{s}$. Whatwas the average force of air resistance?

A crane’s trolley at point P in Fig. 4–63 moves fora few seconds to the right with constant acceleration, and the 870 kg load hangs on a light cable at a$5.0^o$angle to the vertical as shown. What is the acceleration of the trolley and load?

What average force is required to stop a 950-kg car in 8.0 s if the car is traveling at 95 km/h?

When a skier skis down a hill, the normal force exerted on the skier by the hill is

(a) equal to the weight of the skier.

(b) greater than the weight of the skier.

(c) less than the weight of the skier.

If you walk on a log floating on a lake, why does the log move in the opposite direction?

A 75.0 kg person stands on a scale in an elevator. What does the scale read (in N and in kg) when (a) the elevator is at rest, (b) the elevator is climbing at a constant speed of$3.0\mathrm{m}/\mathrm{s}$, (c) the elevator is descending at$3.0\mathrm{m}/\mathrm{s}$(d) the elevator is accelerating upward at$3.0\mathrm{m}/{\mathrm{s}}^2$(e) the elevator is accelerating downward at$3.0\mathrm{m}/{\mathrm{s}}^2$?

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to $21\mathrm{m}/\mathrm{s}\left(75\mathrm{km}/\mathrm{h}\right)$in 12.5 s. Using these data, calculate the maximum steepness of a hill.