One physics question about work/change in energy?

Question

Harold the Hurler is a physics student known for his exceptional baseball pitching arm. To determine the amount of work he performs when throwing a baseball, Harold devises an experiment. He stands at the bottom of a deep pit and hurls a 147-gram baseball through an open third-floor window of a nearby building. Harold's aim is so precise that the ball smoothly enters the tube of the Baseball Absorber, a device he invented and patented. In this device, the ball compresses a spring until it comes momentarily to rest, with the maximum compression recorded at 41.9 cm. The spring has a force constant of 837 N/m, and the position of the baseball's momentary rest is 7.87 m above ground level. Harold starts his pitch from a point in the pit that is 11.1 m below ground level. How much work does Harold perform on the baseball? (Use g = 9.80 m/s² for calculations.)

Anonymous · Accepted Answer

Thank you so much

Anonymous · Answer

There are two places where the energy (work) that has been imparted to the baseball has been stored – in gravitational potential energy (mgh) and in the potential energy of the spring (½kx²).

gravitational potential energy:

m = 0.147 kg

g = 9.8 m/s²

h = 7.87m + 11.1m = 18.97m

mgh = 27.3 J

potential energy of the spring:

k = 837 N/m

x = 0.419 m

½kx² = 73.5 J

Total stored energy when ball comes to rest = 100.8 J

Total work performed on the baseball (assuming zero loss to atmospheric friction) =100.8 J

As a sanity check, the pitch speed is given here by the kinetic energy: 100.8 = ½mv², which rearranges to v = √(100.8 * 2 / m), where m = 0.147 kg. This gives v = 37 m/s, or 83 mph. That’s a long way from record-breaking, but better than I could do!

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One physics question about work/change in energy?

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