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?
Figure4.12.1.A bucket suspended from the back of an accelerating truck.
Explanation4.12.2.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.
(a)Accelerating Downward.
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.
(b)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.
(c)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 skydiver.
SubsectionA*R*C*S Activities
A*R*C*S4.12.3.The Gymnast II.
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.
As part of your symbolic sensemaking (part 3c), use special-case analysis in the case that the two angles are equal to each other.
A*R*C*S4.12.4.The Water Slide.
You go 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 your acceleration.
