Problem 65
A car without ABS (antilock brake system) was moving at \(15.0 \mathrm{~m} / \mathrm{s}\) when the driver hit the brake to make a sudden stop. The coefficients of static and kinetic friction between the tires and the road are 0.550 and 0.430 , respectively. a) What was the acceleration of the car during the interval between braking and stopping? b) How far did the car travel before it stopped?
Problem 68
What coefficient of friction is required to stop a hockey puck sliding at \(12.5 \mathrm{~m} / \mathrm{s}\) initially over a distance of \(60.5 \mathrm{~m} ?\)
Problem 69
A spring of negligible mass is attached to the ceiling of an elevator. When the elevator is stopped at the first floor, a mass \(M\) is attached to the spring, stretching the spring a distance \(D\) until the mass is in equilibrium. As the elevator starts upward toward the second floor, the spring stretches an additional distance \(D / 4\). What is the magnitude of the acceleration of the elevator? Assume the force provided by the spring is linearly proportional to the distance stretched by the spring.
Problem 70
A crane of mass \(M=1.00 \cdot 10^{4} \mathrm{~kg}\) lifts a wrecking ball of mass \(m=1200 .\) kg directly upward. a) Find the magnitude of the normal force exerted on the crane by the ground while the wrecking ball is moving upward at a constant speed of \(v=1.00 \mathrm{~m} / \mathrm{s}\). b) Find the magnitude of the normal force if the wrecking ball's upward motion slows at a constant rate from its initial speed \(v=1.00 \mathrm{~m} / \mathrm{s}\) to a stop over a distance \(D=0.250 \mathrm{~m}\)
Problem 71
4.71 A block of mass \(20.0 \mathrm{~kg}\) supported by a vertical massless cable is initially at rest. The block is then pulled upward with a constant acceleration of \(2.32 \mathrm{~m} / \mathrm{s}^{2}\). a) What is the tension in the cable? b) What is the net force acting on the mass? c) What is the speed of the block after it has traveled \(2.00 \mathrm{m?}\)
Problem 73
A block of mass \(m_{1}=3.00 \mathrm{~kg}\) and a block of mass \(m_{2}=4.00 \mathrm{~kg}\) are suspended by a massless string over a friction less pulley with negligible mass, as in an Atwood machine. The blocks are held motionless and then released. What is the acceleration of the two blocks?
Problem 74
Two blocks of masses \(m_{1}\) and \(m_{2}\) are suspended by a massless string over a frictionless pulley with negligible mass, as in an Atwood machine. The blocks are held motionless and then released. If \(m_{1}=3.50 \mathrm{~kg}\). what value does \(m_{2}\) have to have in order for the system to experience an acceleration \(a=0.400 g\) ? (Hint: There are two solutions to this problem.
Problem 75
A tractor pulls a sled of mass \(M=1000\). kg across level ground. The coefficient of kinetic friction between the sled and the ground is \(\mu_{k}=0.600 .\) The tractor pulls the sled by a rope that connects to the sled at an angle of \(\theta=30.0^{\circ}\) above the horizontal. What magnitude of tension in the rope is necessary to move the sled horizontally with an acceleration \(a=2.00 \mathrm{~m} / \mathrm{s}^{2} ?\)
Problem 76
A \(2.00-\mathrm{kg}\) block is on a plane inclined at \(20.0^{\circ}\) with respect to the horizontal. The coefficient of static friction between the block and the plane is \(0.60 .\) a) How many forces are acting on the block? b) What is the normal force? c) Is this block moving? Explain.
Problem 78
A skydiver of mass \(83.7 \mathrm{~kg}\) (including outfit and equipment) falls in the spread-eagle position, having reached terminal speed. Her drag coefficient is \(0.587,\) and her surface area that is exposed to the air stream is \(1.035 \mathrm{~m}\). How long does it take her to fall a vertical distance of \(296.7 \mathrm{~m} ?\) (The density of air is \(1.14 \mathrm{~kg} / \mathrm{m}^{3}\).)
