How much more kinetic energy does a 6 kg bowling ball have when it is rolling at 16 mph (7.1 m/s) then when it is rolling at 14 mph (6.2 m/s)?
First, we need to calculate the kinetic energy of the bowling ball rolling at 16 mph and 14 mph.
The formula for kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.
At 16 mph or 7.1 m/s:
KE = 1/2 * 6 kg * (7.1 m/s)^2
KE = 151.83 J
At 14 mph or 6.2 m/s:
KE = 1/2 * 6 kg * (6.2 m/s)^2
KE = 108.72 J
The difference in kinetic energy is:
ΔKE = KE (16 mph) - KE (14 mph)
ΔKE = 151.83 J - 108.72 J
ΔKE = 43.11 J
Therefore, the bowling ball has 43.11 J more kinetic energy when rolling at 16 mph compared to rolling at 14 mph.
To find the difference in kinetic energy, we need to calculate the kinetic energy of the bowling ball at each speed and then subtract the lower value from the higher value.
The formula for kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2
First, let's calculate the kinetic energy at 16 mph (7.1 m/s):
Kinetic energy at 16 mph = (1/2) * 6 kg * (7.1 m/s)^2
Kinetic energy at 16 mph = (1/2) * 6 kg * 50.41 m^2/s^2
Kinetic energy at 16 mph = 150.6 J (rounded to one decimal place)
Now, let's calculate the kinetic energy at 14 mph (6.2 m/s):
Kinetic energy at 14 mph = (1/2) * 6 kg * (6.2 m/s)^2
Kinetic energy at 14 mph = (1/2) * 6 kg * 38.44 m^2/s^2
Kinetic energy at 14 mph = 138.4 J (rounded to one decimal place)
Finally, let's find the difference in kinetic energy:
Difference in kinetic energy = Kinetic energy at 16 mph - Kinetic energy at 14 mph
Difference in kinetic energy = 150.6 J - 138.4 J
Difference in kinetic energy = 12.2 J (rounded to one decimal place)
Therefore, the 6 kg bowling ball has approximately 12.2 joules more kinetic energy when rolling at 16 mph (7.1 m/s) compared to when it is rolling at 14 mph (6.2 m/s).