Chapter 5

\(\bullet\) An adventurous archaeologist crosses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Figure 5.38 ). The rope will break if the tension in it exceeds \(2.50 \times 10^{4} \mathrm{N} .\) Our hero's mass is 90.0 \(\mathrm{kg}\) . (a) If the angle \(\theta\) is \(10.0^{\circ}\) , find the tension in the rope. Start with a free-body diagram of the archaeologist. (b) What is the small- est value the angle \(\theta\) can have if the rope is not to break?

\(\bullet$$\bullet\) Tension in a muscle. Muscles are attached to bones by means of tendons. The maximum force that a muscle can exert is directly proportional to its cross-sectional area \(A\) at the widest point. We can express this relationship mathematically as \(F_{\text { max }}=\sigma A,\) where \(\sigma(\) sigma) is a proportionality constant. Surprisingly, \(\sigma\) is about the same for the muscles of all animals. and has the numerical value of \(3.0 \times 10^{5}\) in SI units. (a) What are the SI units of \(\sigma\) in terms of newtons and meters and also in terms of the fundamental quantities \((\mathrm{kg}, \mathrm{m}, \mathrm{s})\) (b) In one set of experiments, the average maximum force that the gastrocne- mius muscle in the back of the lower leg could exert was meas- ured to be 755 \(\mathrm{N}\) for healthy males in their midtwenties. What does this result tell us was the average cross-sectional area, in \(\mathrm{cm}^{2},\) of that muscle for the people in the study?

\(\bullet$$\bullet\) A man pushes on a piano of mass 180 \(\mathrm{kg}\) so that it slides at a constant velocity of 12.0 \(\mathrm{cm} / \mathrm{s}\) down a ramp that is inclined at \(11.0^{\circ}\) above the horizontal. No appreciable friction is acting on the piano. Calculate the magnitude and direction of this push (a) if the man pushes parallel to the incline, (b) if the man pushes the piano up the plane instead, also at 12.0 \(\mathrm{cm} / \mathrm{s}\) paral- lel to the incline, and (c) if the man pushes horizontally, but still with a speed of 12.0 \(\mathrm{cm} / \mathrm{s}\) .

\(\bullet$$\bullet\) Air-bag safety. According to safety standards for air bags, the maximum acceleration during a car crash should not exceed 60\(g\) and should last for no more than 36 ms. (a) In such a case, what force does the air bag exert on a 75 kg person? Start with a free-body diagram. (b) Express the force in part (a) in terms of the person's weight.

\(\bullet$$\bullet\) Forces during chin-ups. People who do chin-ups raise their chin just over a bar (the chinning bar), supporting themselves only by their arms. Typically, the body below the arms is raised by about 30 \(\mathrm{cm}\) in a time of 1.0 s, starting from rest. Assume that the entire body of a 680 N person who is chinning is raised this distance and that half the 1.0 \(\mathrm{s}\) is spent accelerating upward and the other half accelerating downward, uniformly in both cases. Make a free-body dia- gram of the person's body, and then apply it to find the force his arms must exert on him during the accelerating part of the chin-up.

\(\bullet$$\bullet \mathrm{A} 75,600 \mathrm{N}\) spaceship comes in for a vertical landing. From an initial speed of \(1.00 \mathrm{km} / \mathrm{s},\) it comes to rest in 2.00 \(\mathrm{min}\) . with uniform acceleration. (a) Make a free-body diagram of this ship as it is coming in. (b) What braking force must its rockets provide? Ignore air resistance.

\(\bullet$$\bullet\) Force during a jump. An average person can reach a maximum height of about 60 \(\mathrm{cm}\) when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up typically rises a distance of around 50 \(\mathrm{cm} .\) To keep the calculations simple and yet get a reason- able result, assume that the entire body rises this much during the jump. (a) With what initial speed does the person leave the ground to reach a height of 60 \(\mathrm{cm} ?\) (b) Make a free-body diagram of the person during the jump. (c) In terms of this jumper's weight \(W,\) what force does the ground exert on him or her during the jump?

\(\bullet$$\bullet\) A large fish hangs from a spring balance supported from the roof of an elevator. (a) If the elevator has an upward accel- eration of 2.45 \(\mathrm{m} / \mathrm{s}^{2}\) and the balance reads \(60.0 \mathrm{N},\) what is the true weight of the fish? (b) Under what circumstances will the balance read 35.0 \(\mathrm{N} ?\) (c) What will the balance read if the ele- vator cable breaks?

\(\bullet$$\bullet\) A 750.0 -kg boulder is raised from a quarry 125 \(\mathrm{m}\) deep by a long uniform chain having a mass of 575 \(\mathrm{kg}\) . This chain is of uniform strength, but at any point it can support a maximum tension no greater than 2.50 times its weight without breaking. (a) What is the maximum acceleration the boulder can have and still get out of the quarry, and (b) how long does it take to be lifted out at maximum acceleration if it started from rest?

\(\bullet$$\bullet\)The TGV, France's high-speed train, pulls out of the Lyons station and is accelerating uniformly to its cruising speed. Inside one of the cars, a 3.00 \(\mathrm{N}\) digital camera is hanging from the luggage compartment by a light, flexible strap that makes a \(12.0^{\circ}\) angle with the vertical. (a) Make a free-body diagram of this camera. (b) Apply Newton's second law to the camera, and find the acceleration of the train and the tension in the strap.

\(\bullet\) An 80 \(\mathrm{N}\) box initially at rest is pulled by a horizontal rope on a horizontal table. The coefficients of kinetic and static fric- tion between the box and the table are \(\frac{1}{4}\) and \(\frac{1}{2},\) respectively. What is the friction force on this box if the pull is (a) 0 N, (b) \(25 \mathrm{N},(\mathrm{c}) 39 \mathrm{N},(\mathrm{d}) 41 \mathrm{N},(\mathrm{e}) 150 \mathrm{N} ?\)

\(\bullet\) A box of bananas weighing 40.0 \(\mathrm{N}\) rests on a horizontal sur- face. The coefficient of static friction between the box and the surface is \(0.40,\) and the coefficient of kinetic friction is \(0.20 .\) (a) If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on the box? (b) What is the magnitude of the friction force if a monkey applies a hor- izontal force of 6.0 \(\mathrm{N}\) to the box and the box is initially at rest? (c) What minimum horizontal force must the monkey apply to start the box in motion? (d) What minimum horizontal force must the monkey apply to keep the box moving at constant velocity once it has been started?

\(\bullet$$\bullet\) Two crates connected by a rope of negligible mass lie on a horizontal surface. (See Figure \(5.53 .\) ) Crate \(A\) has mass \(m_{A}\) and crate \(B\) has mass \(m_{B}\) . The coefficient of kinetic friction between each crate and the surface is \(\mu_{k .}\) The crates are pulled to the right at a constant velocity of 3.20 \(\mathrm{cm} / \mathrm{s}\) by a horizontal force \(\vec{\boldsymbol{F}} .\) In terms of \(m_{A}, m_{B},\) and \(\mu_{\mathrm{k}},\) calculate (a) the magnitude of the force \(\vec{\boldsymbol{F}}\) and (b) the tension in the rope connecting the blocks. Include the free-body diagram or diagrams you used to determine each answer.

\(\bullet$$\bullet\) A hockey puck leaves a player's stick with a speed of 9.9 \(\mathrm{m} / \mathrm{s}\) and slides 32.0 \(\mathrm{m}\) before coming to rest. Find the coef- ficient of friction between the puck and the ice.

\(\bullet$$\bullet\) Stopping distance of a car. (a) If the coefficient of kinetic friction between tires and dry pavement is \(0.80,\) what is the shortest distance in which you can stop an automobile by lock- ing the brakes when traveling at 29.1 \(\mathrm{m} / \mathrm{s}\) (about 65 \(\mathrm{mi} / \mathrm{h} )\) ? (b) On wet pavement, the coefficient of kinetic friction may be only \(0.25 .\) How fast should you drive on wet pavement in ordel to be able to stop in the same distance as in part (a)? (Note. Locking the brakes is not the safest way to stop.)

\(\bullet$$\bullet\) An \(85-N\) box of oranges is being pushed across a horizon- tal floor. As it moves, it is slowing at a constant rate of 0.90 \(\mathrm{m} / \mathrm{s}\) each second. The push force has a horizontal compo- nent of 20 \(\mathrm{N}\) and a vertical component of 25 \(\mathrm{N}\) downward. Calculate the coefficient of kinetic friction between the box and floor.

\(\bullet$$\bullet\) Rolling friction. Two bicycle tires are set rolling with the same initial speed of 3.50 \(\mathrm{m} / \mathrm{s}\) on a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes 18.1 m; the other is at 105 psi and goes 92.9 \(\mathrm{m} .\) What is the coefficient of rolling friction \(\mu_{\tau}\) for each? Assume that the net horizontal force is due to rolling friction only.

\(\bullet$$\bullet\)A stockroom worker pushes a box with mass 11.2 \(\mathrm{kg}\) on a horizontal surface with a constant speed of 3.50 \(\mathrm{m} / \mathrm{s}\) . The coef- ficients of kinetic and static friction between the box and the surface are 0.200 and \(0.450,\) respectively. (a) What horizontal force must the worker apply to maintain the motion of the box? (b) If the worker stops pushing, what will be the acceler- ation of the box?

\(\bullet$$\bullet\) The coefficients of static and kinetic friction between a 476 \(\mathrm{N}\) crate and the warehouse floor are 0.615 and 0.420 , respectively. A worker gradually increases his horizontal push against this crate until it just begins to move and from then on maintains that same maximum push. What is the acceleration of the crate after it has begun to move? Start with a free-body diagram of the crate.

With its wheels locked, a van slides down a hill inclined at \(40.0^{\circ}\) to the horizontal. Find the acceleration of this van a) if the hill is icy and frictionless, and b) if the coefficient of kinetic friction is \(0.20 .\)

\(\bullet$$\bullet\) A winch is used to drag a 375 \(\mathrm{N}\) crate up a ramp at a con- stant speed of 75 \(\mathrm{cm} / \mathrm{s}\) by means of a rope that pulls parallel to the surface of the ramp. The rope slopes upward at \(33^{\circ}\) above the horizontal, and the coefficient of kinetic friction between the ramp and the crate is 0.25 . (a) What is the tension in the rope? (b) If the rope were suddenly to snap, what would be the accel- eration of the crate immediately after the rope broke?

\(\bullet$$\bullet\) A toboggan approaches a snowy hill moving at 11.0 \(\mathrm{m} / \mathrm{s}\) . The coefficients of static and kinetic friction between the snow and the tobogan are 0.40 and 0.30 , respectively, and the hill slopes upward at \(40.0^{\circ}\) above the horizontal. Find the acceleration of the tobogan (a) as it is going up the hill and (b) after it has reached its highest point and is sliding down the hill.

\(\bullet$$\bullet\) A \(25.0-\mathrm{kg}\) box of textbooks rests on a loading ramp that makes an angle \(\alpha\) with the horizontal. The coefficient of kinetic friction is \(0.25,\) and the coefficient of static friction is 0.35 . (a) As the angle \(\alpha\) is increased, find the minimum angle at which the box starts to slip. (b) At this angle, find the accel- eration once the box has begun to move. (c) At this angle, how fast will the box be moving after it has slid 5.0 \(\mathrm{m}\) along the loading ramp"?

\(\bullet$$\bullet\) A crate of 45.0 -kg tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and ob- serve that the crate just begins to move when your force ex- ceeds 313 \(\mathrm{N}\) . After that you must reduce your push to 208 \(\mathrm{N}\) to keep it moving at a steady 25.0 \(\mathrm{cm} / \mathrm{s}\) . (a) What are the coefficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of 1.10 \(\mathrm{m} / \mathrm{s}^{2}\) (c) Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62 \(\mathrm{m} / \mathrm{s}^{2} .\) (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

\(\bullet$$\bullet\) You are working for a shipping company. Your job is to stand at the bottom of an 8.0 -m-long ramp that is inclined at \(37^{\circ}\) above the horizontal. You grab packages off a conveyor belt and propel them up the ramp. The coefficient of kinetic friction between the packages and the ramp is \(\mu_{k}=0.30\) (a) What speed do you need to give a package at the bottom of the ramp so that it has zero speed at the top of the ramp? (b) Your coworker is supposed to grab the packages as they arrive at the top of the ramp, but she misses one and it slides back down. What is its speed when it returns to you?

What is the acceleration of a raindrop that has reached half of its terminal velocity? Give your answer in terms of \(g .\)

\(\bullet$$\bullet\) An object is dropped from rest and encounters air resist- ance that is proportional to the square of its speed. Sketch qualitative graphs (no numbers) showing (a) the air resistance on this object as a function of its speed, (b) the net force on the object as a function of its speed, (c) the net force on the object as a function of time, (d) the speed of the object as a function of time, and (e) the acceleration of the object as a function of time.

\(\bullet\) You find that if you hang a 1.25 \(\mathrm{kg}\) weight from a vertical spring, it stretches 3.75 \(\mathrm{cm} .\) (a) What is the force constant of this spring in \(\mathrm{N} / \mathrm{m}\) ? (b) How much mass should you hang from the spring so it will stretch by 8.13 \(\mathrm{cm}\) from its original, unstretched length?

\(\bullet\) An unstretched spring is 12.00 \(\mathrm{cm}\) long. When you hang an 875 g weight from it, it stretches to a length of 14.40 \(\mathrm{cm}\) . (a) What is the force constant (in \(\mathrm{N} / \mathrm{m}\) ) of this spring? (b) What total mass must you hang from the spring to stretch it to a total length of 17.72 \(\mathrm{cm} ?\)

\(\bullet\) Heart repair. A surgeon is using material from a donated heart to repair a patient's damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16.0 \(\mathrm{cm}\) strip of the donated aorta reveal that it stretches 3.75 \(\mathrm{cm}\) when a 1.50 \(\mathrm{N}\) pull is exerted on it. (a) What is the force constant of this strip of aortal material? (b) If the maxi- mum distance it will be able to stretch when it replaces the aorta in the damaged heart is \(1.14 \mathrm{cm},\) what is the greatest force it will be able to exert there?

An "extreme" pogo stick utilizes a spring whose uncom- pressed length is 46 \(\mathrm{cm}\) and whose force constant is \(1.4 \times 10^{4} \mathrm{N} / \mathrm{m} . \mathrm{A} 60-\mathrm{kg}\) enthusiast is jumping on the pogo stick, compressing the spring to a length of only 5.0 \(\mathrm{cm}\) at the bottom of her jump. Calculate (a) the net upward force on her at the moment the spring reaches its greatest com- pression and (b) her upward acceleration, in \(\mathrm{m} / \mathrm{s}^{2}\) and \(g^{\prime}\) s at that moment.

\(\bullet\) A light spring having a force constant of 125 \(\mathrm{N} / \mathrm{m}\) is used to pull a 9.50 \(\mathrm{kg}\) sled on a horizontal frictionless ice rink. If the sled has an acceleration of \(2.00 \mathrm{m} / \mathrm{s}^{2},\) by how much does the spring stretch if it pulls on the sled (a) horizontally, (b) at \(30.0^{\circ}\) above the horizontal?

\(\bullet$$\bullet\) Prevention of hip injuries. People (especially the elderly) who are prone to falling can wear hip pads to cushion the impact on their hip from a fall. Experiments have shown that if the speed at impact can be reduced to 1.3 \(\mathrm{m} / \mathrm{s}\) or less, the hip will usually not fracture. Let us investigate the worst-case sce- nario, in which a 55 kg person completely loses her footing (such as on icy pavement) and falls a distance of \(1.0 \mathrm{m},\) the dis- tance from her hip to the ground. We shall assume that the per- son's entire body has the same acceleration, which, in reality, would not quite be true. (a) With what speed does her hip reach the ground? (b) A typical hip pad can reduce the person's speed to 1.3 \(\mathrm{m} / \mathrm{s}\) over a distance of 2.0 \(\mathrm{cm} .\) Find the acceleration (assumed to be constant) of this person's hip while she is slow- ing down and the force the pad exerts on it. (c) The force in part (b) is very large. To see if it is likely to cause injury, calcu- late how long it lasts.

\(\bullet$$\bullet\) You've attached a bungee cord to a wagon and are using it to pull your little sister while you take her for a jaunt. The bungee's unstretched length is \(1.3 \mathrm{m},\) and you happen to know that your little sister weighs 220 \(\mathrm{N}\) and the wagon weighs 75 \(\mathrm{N}\) . Crossing a street, you accelerate from rest to your normal walk- ing speed of 1.5 \(\mathrm{m} / \mathrm{s}\) in 2.0 \(\mathrm{s}\) , and you notice that while you're accelerating, the bungee's length increases to about 2.0 \(\mathrm{m}\) . What's the force constant of the bungee cord, assuming it obeys Hooke's law?

\(\bullet$$\bullet\) Atwood's Machine. A 15.0 -kg load of bricks hangs from one end of a rope that passes over a small, frictionless pulley. A 28.0 -kg counterweight is suspended from the other end of the rope, as shown in Fig. 5.60 . The system is released from rest. (a) Draw two free-body diagrams, one for the load of bricks and one for the counterweight. (b) What is the magnitude of the upward acceleration of the load of bricks? (c) What is the ten- sion in the rope while the load is moving? How does the ten- sion compare to the weight of the load of bricks? To the weight of the counterweight?

\(\bullet$$\bullet\) Friction in an elevator. You are riding in an elevator on the way to the 18 th floor of your dormitory. The elevator is accelerating upward with \(a=1.90 \mathrm{m} / \mathrm{s}^{2} .\) Beside you is the box containing your new computer; the box and its contents have a total mass of 28.0 \(\mathrm{kg} .\) While the elevator is accelerating upward, you push horizontally on the box to slide it at constant speed toward the elevator door. If the coefficient of kinetic friction between the box and the elevator floor is \(\mu_{\mathrm{k}}=0.32\) what magnitude of force must you apply?

\(\bullet$$\bullet\) A 65.0 -kg parachutist falling vertically at a speed of 6.30 \(\mathrm{m} / \mathrm{s}\) impacts the ground, which brings him to a complete stop in a distance of 0.92 \(\mathrm{m}\) (roughly half of his height). Assuming constant acceleration after his feet first touch the ground, what is the average force exerted on the parachutist by the ground?

\(\bullet$$\bullet\) Mars Exploration Rover landings. In January 2004 the Mars Exploration Rover spacecraft landed on the surface of the Red Planet, where the acceleration due to gravity is 0.379 what it is on earth. The descent of this 827 kg vehicle occurred in several stages, three of which are outlined here. In Stage I, friction with the Martian atmosphere reduced the speed from \(19,300 \mathrm{km} / \mathrm{h}\) to 1600 \(\mathrm{km} / \mathrm{h}\) in a 4.0 min interval. In Stage II, a parachute reduced the speed from 1600 \(\mathrm{km} / \mathrm{h}\) to 321 \(\mathrm{km} / \mathrm{h}\) in \(94 \mathrm{s},\) and in Stage III, which lasted 2.5 \(\mathrm{s}\) , retrorockets fired to reduce the speed from 321 \(\mathrm{km} / \mathrm{h}\) to zero. As part of your solu- tion to this problem, make a free-body diagram of the rocket during each stage. Assuming constant acceleration, find the force exerted on the spacecraft (a) by the atmosphere during Stage I, (b) by the parachute during Stage II, and (c) by the retrorockets during Stage III.

the task of designing an accelerometer to be used inside a rocket ship in outer space. Your equipment consists of a very light spring that is \(15.0 \mathrm{~cm}\) long when no forces act to stretch or compress it, \(\begin{array}{lllll}\text { plus } & \text { a } & 1.10 & \text { kg } & \text { weight. }\end{array}\) be attached to a friction- free tabletop, while the \(1.10 \mathrm{~kg}\) weight is attached to the other end, as shown in Figure 5.67 . (Such a spring-type accelerometer system was actually used in the ill-fated Genesis Mission, which collected particles of the solar wind. Unfortunately, because it was installed backward, it did not measure the acceleration correctly during the craft's descent to earth. As a result, the parachute failed to open and the capsule crashed on Sept. \(8,2004 .)\) (a) What should be the force constant of the spring so that it will stretch by \(1.10 \mathrm{~cm}\) when the rocket accelerates forward at \(2.50 \mathrm{~m} / \mathrm{s}^{2}\) ? Start with a free-body diagram of the weight. (b) What is the acceleration (magnitude and direction) of the rocket if the spring is compressed by \(2.30 \mathrm{~cm} ?\)

\(\bullet$$\bullet\) A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is set moving. The coefficients of kinetic and static friction between the box and the bed of the truck are 0.355 and 0.650 , respectively. Starting from rest, what is the shortest time this truck could accelerate uniformly to 30.0 \(\mathrm{m} / \mathrm{s}(\approx 60 \mathrm{mph})\) without causing the box to slide. Include a free-body diagram of the toolbox as part of your solution. (Hint: First use Newton's second law to find the maximum acceleration that static friction can give the box, and then solve for the time required to reach 30.0 \(\mathrm{m} / \mathrm{s} .\) )

\(\bullet$$\bullet\) Accident analysis. You have been called to testify as an expert witness in a trial involving an automobile accident. The speed limit on the highway where the accident occurred was 40 mph. The driver of the car slammed on his brakes, locking his wheels, and left skid marks as the car skidded to a halt. You measure the length of these skid marks to be \(219 \mathrm{ft}, 9\) in. and determine that the coefficient of kinetic friction between the wheels and the pavement at the time of the accident was \(0.40 .\) How fast was this car traveling (to the nearest number of mph) just before the driver hit his brakes? Was he guilty of speeding?

\(\bullet$$\bullet\) You push with a horl- zontal fonce of 50 \(\mathrm{N}\) against a 20 \(\mathrm{N}\) box, press- ing it against a rough ver- tical wall to hold it in place, The coefficients of kinetic and static friction between this box and the wall are 0.20 and 0.50 , respectively. (a) Make a free-body diagram of this box. (b) What is the friction force on the box? (c) How hard would you have to press for the box to slide downward with a uni- form speed of 10.5 \(\mathrm{cm} / \mathrm{s}\) ?

\(\bullet$$\bullet\) Some sliding rocks approach the base of a hill with a speed of 12 \(\mathrm{m} / \mathrm{s}\) . The hill rises at \(36^{\circ}\) above the horizontal and has coefficients of kinetic and static friction of 0.45 and 0.65 . respectively, with these rocks. Start each part of your solution to this problem with a free-body diagram. (a) Find the acceler- ation of the rocks as they slide up the hill. (b) Once a rock reaches its highest point, will it stay there or slide down the hill? If it stays there, show why. If it slides down, find its accel- cration oa the way down.

\(\bullet$$$\bullet\) Elevator design. You are designing an elevator for a hos- pital. The force exerted on a passenger by the floor of the ele- vator is not to exceed 1.60 times the passenger's weight. The elevator accelerates upward with constant acceleration for a distance of 3.0 m and then starts to slow down. What is the maximum speed of the elevator?

\(\bullet$$\bullet\) At night while it is dark, a driver inadvertently parks his car on a drawbridge. Some time later, the bridge must be raised to allow a boat to pass through. The coefficients of fric- tion between the bridge and the car's tires are \(\mu_{\mathrm{s}}=0.750\) and \(\mu_{\mathrm{k}}=0.550 .\) Start each part of your solution to this problem with a free-body diagram of the car. (a) At what angle will the car just start to slide? (b) If the bridge attendant sees the car suddenly start to slide and immediately turns off the bridge's motor, what will be the car's acceleration after it has begun to move?

\(\bullet$$\bullet\) The monkey and her bananas. \(\Lambda 20 \mathrm{kg}\) monkey has a firm hold on a light rope that passes over a frictionless pulley and is attached to a 20 \(\mathrm{kg}\) bunch of bananas (Figure 5.72 ). The monkey looks up, sees the bananas, and starts to climb the rope to get them. (a) As the monkey climbs, do the bananas move up, move down, or remain at rest? (b) As the monkey climbs, does the distance between the monkey and the ba- nanas decrease, increase, or remain con- stant? (c) The monkey releases her hold on - the rope. What happens to the distance be- tween the monkey and the bananas while she is falling? (d) Before reaching the ground, the monkey grabs the rope to stop her fall. What do the bananas do?

If the toboggan is well waxed so that there is no friction, what force does the sail have to provide to move the student-filled toboggan up the hill at a constant velocity (once it gets started)? \(\begin{array}{l}{\text { A. } g \sin \alpha} \\ {\text { B. } w \sin \alpha} \\\ {\text { C. } w} \\ {\text { D. } w g \sin \alpha}\end{array}\)