A steel ball weighing 128 pounds (mass= 4 slugs) is suspended from a spring. This stretches the spring 128/485 feet.

The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second.
The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) .

Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)

Take as the gravitational acceleration 32 feet per second per second.

When using English units (lb, ft, etc.) you need to be a bit careful with equations involving mass. Pounds (lb) is a unit of force, not mass. Using mg=F and g=32 ft/sec^2 we see that if an object weights L pounds it will have a mass of L/32 lb*sec^2/ft (or slugs).

Solution Summary

This is an example of a problem regarding mechanical displacement of a steel ball. The answer is attached in two JPG files, where the Expert has written their response using step by step calculations and diagrams to aid understanding of the problem.

A hollow steelball weighing 4 pounds (mass = 1/8 slugs) is suspended from a spring. This stretches the spring 1/6 feet. The ball is started in motion from the equilibrium position with a downward velocity of 8 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet pe

Run a simulation of a ball dropping and measure the displacement, velocity and acceleration.
1. Measure the time that it takes the ball to travel 1 meter, 2 meters, 3 meters and each succeeding meter up to 6 meters for the Earth and the Moon.
2. Graph the distance traveled versus the time for the Earth and the Moon.
3

It is not uncommon during the service of a professional tennis player for the racket to exert an average force of 156.0 N on the ball. If the ball has a mass of 0.070 kg and is in contact with the strings of the racket for 0.030 s, what is the kinetic energy of the ball as it leaves the racket? Assume that the ball starts from r

A steelball with mass 38.0 g is dropped from a height of 1.93 m onto a horizontal steel slab. The ball rebounds to a height of 1.56 m .Calculate the impulse delivered to the ball during impact. If the ball is in contact with the slab for a time of 2.40 ms, find the average force on the ball during impact.

At serve a tennis player aims to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.89 m high net about L=14.8 m from the server if the ball is "launched" from a height of H=2.39 m?

A hanging wire has a length of 1.90m. When a steelball of mass 50.0kg is suspended from the wire, the wire stretches by 2.30mm .
If the ball is pulled down a small additional distance and released, at what frequency will it vibrate?
Assume that the stress on the wire is less than the proportional limit.
Take the free fal

Twenty-five samples of steel beam were chosen and tested for Young's Modulus. Eight had a modulus of E = 30 x 10^6 psi. Two had a modulus of E = 29 x 10^6 psi. Fifteen had a modulus of E = 30. x 1-^6 psi.
Estimate the following probabilities:
i) P {E > 29.5 x 10^6 psi}
ii) P {E > 30 x 10^6 psi}
iii) P{E > 28 x 10^6 psi}

See attachment.
A 126 g ball is dropped from a height of 64.9 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.48716 cm. The acceleration of gravity is 9.8 m/s2.
Calculate the spring force costant k. Answer in units of N/m

A small steelball is rolled down an inclined plane from a table. The inclined plane is a slotted ruler. One end of the ruler is 10cm off of the table. The ball leaves the table horizontally and lands 46cm from the table on the floor. The table is 72 cm from the ground.
1. Using projectile motion equations, determine the spee