A cricket bowler can bowl a 162 g ball at 149 km/hr. Calculate the kinetic energy of this bowl and use this to compare to a bowling ball that weighs 6 kg. How fast would the bowling ball need to be bowled to have the same kinetic energy as the cricket ball? (Answer to 1dp)
To calculate the kinetic energy of the cricket ball, we can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
First, let's convert the mass of the cricket ball from grams to kilograms. We divide 162 grams by 1000 to get the mass in kilograms:
Mass = 162 g / 1000 = 0.162 kg
Now, we can plug in the values to find the kinetic energy of the cricket ball:
Kinetic Energy (cricket ball) = (1/2) * 0.162 kg * (149 km/hr)^2
Before we proceed, we need to convert the velocity from kilometers per hour (km/hr) to meters per second (m/s) since the formula requires the velocity in meters per second:
Velocity (m/s) = 149 km/hr * (1000 m/1 km) * (1 hr/3600 s)
Simplifying this calculation, we find:
Velocity (m/s) = 149 * 1000 / 3600 = 41.389 m/s
Now, we substitute the values into the kinetic energy formula and calculate:
Kinetic Energy (cricket ball) = (1/2) * 0.162 kg * (41.389 m/s)^2
Kinetic Energy (cricket ball) ≈ 0.5 * 0.162 * 41.389^2 ≈ 135.775 J
The kinetic energy of the cricket ball is approximately 135.775 joules.
To compare this to a bowling ball, we can use the same formula. Given that the weight of the bowling ball is 6 kg, we need to find the velocity at which it needs to be bowled to have the same kinetic energy as the cricket ball. We will use the following formula:
Kinetic Energy (bowling ball) = (1/2) * 6 kg * (velocity^2)
To find the velocity, we rearrange the formula:
velocity = √((2 * kinetic energy) / mass)
Substituting the values, we can calculate:
velocity = √((2 * 135.775) / 6) ≈ 7.47 m/s
Therefore, the bowling ball would need to be bowled at approximately 7.47 m/s to have the same kinetic energy as the cricket ball.