A truck is traveling in a straight line on level ground, and is accelerating uniformly. Two ropes are tied to the back of the truck. The other end of each rope is tied to a bucket: the bucket tied to rope 1 has a larger mass than the bucket tied to rope 2. You notice that each rope is hanging from the back of the truck at a fixed (but potentially different) angle. Is the angle of rope 1 greater than, less than, or equal to the angle of rope 2?
Figure4.10.1.A bucket suspended from the back of an accelerating truck.
Explanation4.10.2.Skydiver.
When a skydiver jumps from a plane, they quickly become subject to a substantial force known as air resistance or air drag. This force becomes larger when the skydiver’s velocity becomes larger.
During the first part of falling, the skydiver is accelerating downward. Draw and label a freebody diagram for the skydiver. Rank the magnitudes of all forces on the skydiver.
(a)Constant Velocity.
Eventually, the skydiver stops accelerating and moves with constant velocity (this is known as terminal velocity). Draw and label a free-body diagram for the skydiver. Rank the magnitudes of all forces on the skydiver.
(b)Throwing an Object.
Suppose the skydiver throws an object downward so that the object’s speed is greater than the terminal velocity, with respect to the ground. In this situation, the acceleration of the object will be upward. Draw and label a free-body diagram for the object. Rank the magnitudes of all forces on the object.
Explanation4.10.3.Water Slide.
You slide down a water slide of length \(L\) that makes an angle \(\theta\) with the horizontal, starting from rest. Do not neglect friction (use \(\mu_k\) as the coefficient of kinetic friction). Determine the amount of time it takes you to reach the bottom of the slide.
To make sense of your answer, use special-case analysis in the case that friction can be neglected.
A*R*C*S4.10.4.Walking a Cat.
You are trying to exercise your cat by walking them around the room with a harness - a jacket is strapped around the cat with a leash that you can pull. To get your cat moving, you pull on the leash at an angle \(\theta\) above the horizontal (note this is not how you should train your cat with a harness). Annoyed, your cat flops onto their side where there is a sizable friction between the cat and the floor. As you pull your cat, you notice they move with a constant speed.
From previous experiments with this harness, you know that your "pull" at the given angle has a vertical component equal to half the weight of your cat.
(a)Rank the forces.
During the pull, rank the magnitude of the forces acting on the cat.
To assist you, you add an additional rope hanging from the ceiling that always stays vertical but the attachment is free to move along the ceiling (like something you would find in an action movie). This new rope’s tension has a magnitude equal to the vertical component of your pull. You now pull on the leash with the same magnitude and direction as before.
(b)Explain.
Now, you notice the cat speeds up. Explain why this occurs.
SubsectionA*R*C*S Activities
A*R*C*S4.10.5.The Gymnast.
A gymnast is training by hanging from two ropes attached to the ceiling, as shown in the figure. The angles \(\theta\) and \(\alpha\) are different. The gravitational force on the gymnast is 750 N downward. Determine the magnitude of the tension in each rope.
