Problem 53
An engine block of mass \(M\) is on the flatbed of a pickup truck that is traveling in a straight line down a level road with an initial speed of \(30.0 \mathrm{~m} / \mathrm{s}\). The coefficient of static friction between the block and the bed is \(\mu_{s}=0.540 .\) Find the minimum distance in which the truck can come to a stop without the engine block sliding toward the cab.
Problem 54
A box of books is initially at rest a distance \(D=0.540 \mathrm{~m}\) from the end of a wooden board. The coefficient of static friction between the box and the board is \(\mu_{s}=0.320\), and the coefficient of kinetic friction is \(\mu_{k}=0.250 .\) The angle of the board is increased slowly, until the box just begins to slide; then the board is held at this angle. Find the speed of the box as it reaches the end of the board. -4.55 A block of mass \(M_{1}=0.640 \mathrm{~kg}\) is initially at rest on a cart of mass \(M_{2}=0.320 \mathrm{~kg}\) with the cart initially at rest on a level air track. The coefficient of static friction between the block and the cart is \(\mu_{s}=0.620\), but there is essentially no friction between the air track and the cart. The cart is accelerated by a force of magnitude \(F\) parallel to the air track. Find the maximum value of \(F\) that allows the block to accelerate with the cart, without sliding on top of the cart.
Problem 55
A block of mass \(M_{1}=0.640 \mathrm{~kg}\) is initially at rest on a cart of mass \(M_{2}=0.320 \mathrm{~kg}\) with the cart initially at rest on a level air track. The coefficient of static friction between the block and the cart is \(\mu_{s}=0.620\), but there is essentially no friction between the air track and the cart. The cart is accelerated by a force of magnitude \(F\) parallel to the air track. Find the maximum value of \(F\) that allows the block to accelerate with the cart, without sliding on top of the cart.
Problem 56
offee filters behave Ince small parachutes, with a drag force that is proportional to the velocity squared, \(F_{\text {drag }}=K v^{2}\). A single coffee filter, when dropped from a height of \(2.0 \mathrm{~m}\), reaches the ground in a time of \(3.0 \mathrm{~s}\). When a second coffee filter is nestled within the first, the drag force remains the same, but the weight is doubled. Find the time for the combined filters to reach the ground. (Neglect the brief period when the filters are accelerating up to their terminal speed.)
Problem 57
4.57 Your refrigerator has a mass of \(112.2 \mathrm{~kg}\), including the food in it. It is standing in the middle of your kitchen, and you need to move it. The coefficients of static and kinetic friction between the fridge and the tile floor are 0.460 and 0.370 , respectively. What is the magnitude of the force of friction acting on the fridge, if you push against it horizontally with a force of each magnitude? a) \(300 \mathrm{~N}\) b) \(500 \mathrm{~N}\) c) \(700 \mathrm{~N}\)
Problem 58
On the bunny hill at a ski resort, a towrope pulls the skiers up the hill with constant speed of \(1.74 \mathrm{~m} / \mathrm{s}\). The slope of the hill is \(12.4^{\circ}\) with respect to the horizontal. A child is being pulled up the hill. The coefficients of static and kinetic friction between the child's skis and the snow are 0.152 and 0.104 , respectively, and the child's mass is \(62.4 \mathrm{~kg}\), including the clothing and equipment. What is the force with which the towrope has to pull on the child?
Problem 59
A skier starts with a speed of \(2.0 \mathrm{~m} / \mathrm{s}\) and skis straight down a slope with an angle of \(15.0^{\circ}\) relative to the horizontal. The coefficient of kinetic friction between her skis and the snow is \(0.100 .\) What is her speed after 10.0 s?
Problem 60
\(\bullet 4.60\) A block of mass \(m_{1}=21.9 \mathrm{~kg}\) is at rest on a plane inclined at \(\theta=30.0^{\circ}\) above the horizontal. The block is connected via a rope and massless pulley system to another block of mass \(m_{2}=25.1 \mathrm{~kg}\), as shown in the figure. The coefficients of static and kinetic friction between block 1 and the inclined plane are \(\mu_{s}=0.109\) and \(\mu_{k}=0.086\) respectively. If the blocks are released from rest, what is the displacement of block 2 in the vertical direction after 1.51 s? Use positive numbers for the upward direction and negative numbers for the downward direction.
Problem 61
A wedge of mass \(m=36.1 \mathrm{~kg}\) is located on a plane that is inclined by an angle \(\theta=21.3^{\circ}\) with respect to the horizontal. A force \(F=302.3 \mathrm{~N}\) in the horizontal direction pushes on the wedge, as shown in the figure. The coefficient of kinetic friction between the wedge and the plane is 0.159 What is the acceleration of the wedge along the plane?
Problem 62
A chair of mass \(M\) rests on a level floor, with a coef. ficient of static friction \(\mu_{s}=0.560\) between the chair and the floor. A person wishes to push the chair across the floor. He pushes on the chair with a force \(F\) at an angle \(\theta\) below the horizontal. What is the maximum value of \(\theta\) for which the chair will not start to move across the floor?
