How Does Compression Affect the Kinetic Energy of a Bowling Ball?

[Cummings]

Physics students are testing an old bed spring which is compressed 4cm when a force of 4 N is applied. This spring is secured to a wall and a bowling ball of 4kg is roled into it so that it hits at a speed of 2m/s

1. Calculate the compression of the spring when the speed of the ball has been reduced to 1m/s by the spring

2. What is the value of the compression force when the speed of the ball is 1.9 ms to the right?

3. Calculate the compression of the spring what the ball has momentarily come to rest.

For the first question:
the kinetic energy of the ball at 2ms = .5 * 4 * (2 squared) = 8 N
the kinetic energy of the ball at 1ms = .5 * 4 * (1 squared) = 2 N

thus the kinetic energy transferred to the spring is 6 N

Now, .5k(x squared) gives us the potential energy in the spring.
so 6 = .5k(x squared)
k is the spring ocnstand which can be taken from 4N/.04 Meters = 100
6 = 50(x squared)
X = Square root of (6/50)
= .346 meters = 34.6 cm?

thats all i can get at the mo..i need help :)

 

[HallsofIvy]

Actually, you've done the hard part! Yes, subtracting the two kinetic energies gives the increase in potential energy and you have calculated the amount of compression correctly.

For Problem 2 repeat your solution to problem 1, using 1.9 m/s instead of 1 m/s for the final velocity. Once you have found the amount of compression, multiply that by k (force= k*compression) to find the force asked for.

For Problem 3, do the same as for problem 2 except that, now, the final velocity is 0 m/s. Find the compression as you did in problem 1 and then multiply by k to find the force.

 

[FZ+]

Uh... note though that the units of energy are Joules, or J, not Newtons (N).

 

[Cummings]

FZ+ yes true that..Jouls not Newtons just another simple error.

From the textbook i was working out of, it said it was 3.5cm compression, not 35cm so i think that would just be another typo.