魅影直播

A 28.0-kg block is connected to an empty 2.00-kg bucket by a cord running over a frictionless pulley (Fig. 4鈥�73). The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and the block is 0.32. Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket. (b) Calculate the acceleration of the system. Ignore mass of cord.

A 72-kg water skier is being accelerated by a ski boat on a flat (鈥済lassy鈥�) lake. The coefficient of kinetic friction between the skier鈥檚 skis and the water surface is ${渭}_k=0.25$(Fig. 4鈥�74). (a) What is the skier鈥檚 acceleration if the rope pulling the skier behind the boat applies a horizontal tension force of magnitude$F_T=240\mathrm{N}$to the skier$\left(胃=0掳\right)$? (b) What is the skier鈥檚 horizontal acceleration if the rope pulling the skier exerts a force of$F_T=240\mathrm{N}$on the skier at an upward angle$胃=12掳$? (c) Explain why the skier鈥檚 acceleration in part (b) is greater than that in part (a).

A 75-kg snowboarder has an initial velocity of at the top of a 28掳 incline (Fig. 4鈥�75). After sliding down the 110-m-long incline (on which the coefficient of kinetic friction is${渭}_k=0.18$), the snowboarder has attained a velocity v. The snowboarder then slides along a flat surface (on which${渭}_k=0.15$) and comes to rest after a distance x. Use Newton鈥檚 second law to find the snowboarder鈥檚 acceleration while on the incline and while on the flat surface. Then use these accelerations to determine x.

(a) If the horizontal acceleration produced briefly by an earthquake is a, and if an object is going to 鈥渉old its place鈥� on the ground, show that the coefficient of static friction with the ground must be at least${渭}_s=\frac{a}{g}$. (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to$4\mathrm{m}/{\mathrm{s}}^2$in the San Francisco Bay Area. Would a chair have started to slide on a floor with coefficient of static friction 0.25?

Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle$胃$to the horizontal, Fig. 4鈥�76 (block B is above block A). The masses of the blocks are$m_{\mathrm{A}}$and$m_{\mathrm{B}}$, and the coefficients of friction are${渭}_{\mathrm{A}}$and${渭}_{\mathrm{B}}$. If$m_{\mathrm{A}}=m_{\mathrm{B}}=5\mathrm{kg}$and${渭}_{\mathrm{A}}=0.20$and${渭}_{\mathrm{B}}=0.30$, determine (a) the acceleration of the blocks and (b) the tension in the cord, for an angle$胃=32掳$.

A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the sloping road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction. (b) Assume an effective coefficient of friction equal to 0.10.

A 65-kg ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is${渭}_{\mathrm{k}}=0.10$, how fast was she moving at the start of her coast?

An 18-kg child is riding in a child-restraint chair, securely fastened to the seat of a car (Fig. 4鈥�77). Assume the car has speed 45 km/h when it hits a tree and is brought to rest in 0.20 s. Assuming constant deceleration during the collision, estimate the net horizontal force F that the straps of the restraint chair exert on the child to hold her in the chair.

FIGURE 4-77Problem 97