Exam 6: Dynamics I: Motion Along a Line

In the figure, a T-bar ski tow pulls a skier up a hill inclined at 10° above horizontal. The skier starts from rest and is pulled by a cable that exerts a tension T at an angle of 30° above the surface of the hill. The mass of the skier is 60 kg and the effective coefficient of kinetic friction between the skis and the snow is 0.100. What is the maximum tension in the cable if the starting acceleration is not to exceed 0.400 g?

A 50.0-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.300 and the coefficient of kinetic friction is 0.200. What is the friction force on the box if (a) a horizontal 140-N push is applied to it? (b) a horizontal 175-N push is applied to it?

Kieran takes off from rest down a 50 m high, 10° slope on his jet-powered skis. The skis have a thrust of 280 N parallel to the surface of the slope. The combined mass of skis and Kieran is 50 kg (the fuel mass is negligible). Kieran's speed at the bottom is 40 m/s. What is the coefficient of kinetic friction of his skis on snow?

When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal speed. Once he has reached terminal speed

A 6.0 kg box slides down an inclined plane that makes an angle of 39° with the horizontal. If the coefficient of kinetic friction is 0.19, at what rate does the box accelerate down the slope?

A fish weighing 16 N is weighed using two spring scales, each of negligible weight, as shown in the figure. What will be the readings of the scales?

Jason takes off from rest across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.10. Unfortunately, the skis run out of fuel after only 67 s. How far has Jason traveled when he finally coasts to a stop?

An object weighing 4.00 N falls from rest subject to a frictional drag force given by F_drag = bv², where v is the speed of the object and What terminal speed will this object approach?

A factory robot drops a 10 kg computer onto a conveyor belt running at 3.1 m/s. The materials are such that μ_s = 0.50 and μ_k = 0.30 between the belt and the computer. How far is the computer dragged before it is riding smoothly on the belt?

A box slides down a frictionless plane inclined at an angle θ above the horizontal. The gravitational force on the box is directed

The following four forces act on a 4.00 kg object: ₁ = 300 N east ₂ = 700 N north ₃ = 500 N west ₄ = 600 N south What is the acceleration of the object?

A traffic light weighing 100 N is supported by two ropes as shown in the figure. The tensions in the ropes are closest to

A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are μ_s = 0.40 and μ_k = 0.30, respectively. The puck's initial speed is 4.9 m/s. What speed does it have when it slides back down to its starting point?

15) Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200-kg car (a so-called compact model) to a rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). (Bumpers are built with springs that compress to provide a stopping force without, hopefully, denting the metal.)

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above the horizontal. If T is the tension in this wire, then

A 1000-kg car is driving toward the north along a straight horizontal road at a speed of 20.0 m/s. The driver applies the brakes and the car comes to a rest uniformly in a distance of 200 m. What are the magnitude and direction of the net force applied to the car to bring it to rest?

A 10,000-kg rocket blasts off from earth with a uniform upward acceleration of 2.00 m/s² and feels no air resistance. The upward thrust force its engines must provide during this acceleration is closest to

The magnitude of the drag force of air resistance on a certain 20.0-kg object is proportional to its speed. If the object has a terminal speed 80.0 m/s, what is the magnitude of the drag force on the object when it is falling with a speed 30.0 m/s?

A 1.20-kg ball is hanging from the end of a rope. The rope hangs at an angle 25.0° from the vertical when a 15.0 m/s horizontal wind is blowing. If the wind's force on the rope is negligible, what drag force does the wind exert on the ball?

A ship is being pulled through a harbor at constant velocity by two tugboats as shown in the figure. The lines attached to the two tugboats have the same tension of 200,000 N. Each line makes an angle of 28.0° with the direction the ship is being towed. What is the magnitude of the drag force due to the water on the ship?