Problem 20
A 550-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is 850 kg. As the elevator starts moving, the scale reads 450 N. (a) Find the acceleration of the elevator (magnitude and direction). (b) What is the acceleration if the scale reads 670 N? (c) If the scale reads zero, should the student worry? Explain. (d) What is the tension in the cable in parts (a) and (c)?
Problem 21
When jumping straight up from a crouched position, an average person can reach a maximum height of about 60 cm. During the jump, the person's body from the knees up typically rises a distance of around 50 cm. To keep the calculations simple and yet get a reasonable 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 cm? (b) Draw 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?
Problem 22
A 2540-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force such that its vertical velocity as a function of time is given by \(v(t) = At + Bt^2\), where \(A\) and \(B\) are constants and time is measured from the instant the fuel is ignited. The rocket has an upward acceleration of 1.50 m/s\(^2\) at the instant of ignition and, 1.00 s later, an upward velocity of 2.00 m>s. (a) Determine \(A\) and \(B\), including their SI units. (b) At 4.00 s after fuel ignition, what is the acceleration of the rocket, and (c) what thrust force does the burning fuel exert on it, assuming no air resistance? Express the thrust in newtons and as a multiple of the rocket's weight. (d) What was the initial thrust due to the fuel?
Problem 23
A 2.00-kg box is moving to the right with speed 9.00 m/s on a horizontal, frictionless surface. At \(t =\) 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude \(F(t) = (6.00 N/s^2)t^2\). (a) What distance does the box move from its position at \(t =\) 0 before its speed is reduced to zero? (b) If the force continues to be applied, what is the speed of the box at \(t =\) 3.00 s?
Problem 24
A 5.00-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force \(F(t)\) is applied to the end of the rope, and the height of the crate above its initial position is given by \(y(t) =\) (2.80 m/s)\(t +\) (0.610 m/s\(^3\))\(t^3\). What is the magnitude of F when \(t =\) 4.00 s?
Problem 25
After emergencies with major blood loss, a patient is placed in the Trendelenburg position, in which the foot of the bed is raised to get maximum blood flow to the brain. If the coefficient of static friction between a typical patient and the bedsheets is 1.20, what is the maximum angle at which the bed can be tilted with respect to the floor before the patient begins to slide?
Problem 27
A stockroom worker pushes a box with mass 16.8 kg on a horizontal surface with a constant speed of 3.50 m/s. The coefficient of kinetic friction between the box and the surface is 0.20. (a) What horizontal force must the worker apply to maintain the motion? (b) If the force calculated in part (a) is removed, how far does the box slide before coming to rest?
Problem 28
A box of bananas weighing 40.0 N rests on a horizontal surface. 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 it? (b) What is the magnitude of the friction force if a monkey applies a horizontal force of 6.0 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? (e) If the monkey applies a horizontal force of 18.0 N, what is the magnitude of the friction force and what is the box's acceleration?
Problem 29
A 45.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0 cm/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 m/s\(^2\)? (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is 1.62 m/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)?
Problem 30
Some sliding rocks approach the base of a hill with a speed of 12 m/s. The hill rises at 36\(^\circ\) above the horizontal and has coefficients of kinetic friction and static friction of 0.45 and 0.65, respectively, with these rocks. (a) Find the acceleration 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, show why. If it slides, find its acceleration on the way down.
