a .300 kg baseball is thrown at a speed of 6.5m/s. the batter hits the ball and it flies into the outfield at a speed of 19.2 m/s. How much work is done into hitting the baseball
work in = change in kinetic energy
= (1/2)m(v2^2 -v1^2)
((1/2)M(Vf^2))-((1/2)M(Vi^2))
To calculate the work done in hitting the baseball, we need to know the change in kinetic energy of the baseball.
The initial kinetic energy of the baseball is given by:
KE(initial) = (1/2) * mass * (initial velocity)^2
Given:
Mass of the baseball (m) = 0.300 kg
Initial velocity of the baseball (vi) = 6.5 m/s
So,
KE(initial) = (1/2) * 0.300 kg * (6.5 m/s)^2
Next, we calculate the final kinetic energy of the baseball after being hit:
KE(final) = (1/2) * mass * (final velocity)^2
Given:
Final velocity of the baseball (vf) = 19.2 m/s
So,
KE(final) = (1/2) * 0.300 kg * (19.2 m/s)^2
The work done in hitting the baseball is equal to the change in kinetic energy, which can be calculated by subtracting the initial kinetic energy from the final kinetic energy:
Work = KE(final) - KE(initial)
Substituting the values, we can calculate the work done:
Work = [(1/2) * 0.300 kg * (19.2 m/s)^2] - [(1/2) * 0.300 kg * (6.5 m/s)^2]
Now, we can simplify and calculate the work.
To determine the work done in hitting the baseball, we need to calculate the change in kinetic energy of the baseball.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Initial kinetic energy = (1/2) * mass * initial velocity^2
Final kinetic energy = (1/2) * mass * final velocity^2
The change in kinetic energy can be calculated as:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Now let's substitute the values into the formula:
Mass of the baseball (m) = 0.300 kg
Initial velocity (v1) = 6.5 m/s
Final velocity (v2) = 19.2 m/s
Initial kinetic energy = (1/2) * 0.300 kg * (6.5 m/s)^2
Final kinetic energy = (1/2) * 0.300 kg * (19.2 m/s)^2
Change in kinetic energy = [(1/2) * 0.300 kg * (19.2 m/s)^2] - [(1/2) * 0.300 kg * (6.5 m/s)^2]
Calculate the change in kinetic energy to find the work done in hitting the baseball.