A baseball player pitches a 0.14kg baseball at 30m/s. How much work did the player do to the ball to give it this energy?
kinetic energy = input work = (1/2) m v^2
= 0.07 * 900 = 63 Joules
To calculate the work done by the baseball player to give the ball its energy, we can use the formula for work:
Work = force x distance
In this case, the force exerted by the baseball player is the force required to accelerate the ball to its final velocity. This force can be calculated using Newton's second law of motion:
Force = mass x acceleration
Where the mass is the mass of the baseball, which is given as 0.14 kg, and the acceleration is the change in velocity divided by the time taken. Since no time is given, we assume that the change in velocity occurs instantaneously. Therefore, the acceleration is equal to the final velocity.
Acceleration = final velocity = 30 m/s
Now, we can calculate the force:
Force = mass x acceleration
= 0.14 kg x 30 m/s
= 4.2 N
Finally, we can calculate the work done:
Work = force x distance
The distance is not given in the question, so we cannot determine the exact work done. To find the work, we need to know the distance over which the force is applied to accelerate the ball.
To calculate the work done by the baseball player on the baseball, we can use the formula for work:
Work = Force x Distance
To find the force, we can use Newton's second law of motion, which states:
Force = Mass x Acceleration
The acceleration of the baseball can be calculated using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
In this case, the initial velocity is 0 m/s as the pitcher throws the ball from rest. The final velocity is 30 m/s, and we assume that the time taken to reach this velocity is negligible.
Now we have all the values needed to calculate the work:
Mass of the baseball (m) = 0.14 kg
Initial Velocity (u) = 0 m/s
Final Velocity (v) = 30 m/s
First, let's calculate the acceleration using the formula:
Acceleration (a) = (v - u) / t = (30 - 0) / t ≈ (30) / t
Since we assume the time is negligible, we can approximate the acceleration as a very large value.
Next, let's find the force using Newton's second law:
Force (F) = m x a = 0.14 kg x (30 / t) ≈ (30 x 0.14 kg) / t ≈ 4.2 / t
Now, substitute the force into the work formula:
Work = Force x Distance
Since we don't have the distance, it is impossible to calculate the exact work done without additional information about the distance the ball traveled. The work done depends on the distance over which the force was applied.