How much more kinetic energy does a 6-kilogram bowling ball have when it is rolling at 16 mph (7.1 meters per second) than when it is rolling at 14 mph (6.2 meters per second)?
KE=12mv2
To calculate the difference in kinetic energy, we need to find the kinetic energy at both speeds using the formula KE = 1/2mv^2 and then subtract the lower kinetic energy from the higher one.
For the first speed of 16 mph (7.1 m/s):
KE1 = 1/2 * 6 kg * (7.1 m/s)^2
KE1 = 1/2 * 6 kg * 50.41 m^2/s^2
KE1 = 150.63 kg * m^2/s^2
For the second speed of 14 mph (6.2 m/s):
KE2 = 1/2 * 6 kg * (6.2 m/s)^2
KE2 = 1/2 * 6 kg * 38.44 m^2/s^2
KE2 = 115.32 kg * m^2/s^2
The difference in kinetic energy is:
ΔKE = KE1 - KE2
ΔKE = 150.63 kg * m^2/s^2 - 115.32 kg * m^2/s^2
ΔKE = 35.31 kg * m^2/s^2
Therefore, the 6-kilogram bowling ball has 35.31 kg * m^2/s^2 more kinetic energy when it is rolling at 16 mph compared to when it is rolling at 14 mph.