A baseball pitcher throws a 250g baseball to make it accelerate to 50 m/s the instant that it leaves his hand. How much energy (in Joules) is expended (how much work is done) if that same baseball travels a distance of 30 meters?
Choose the best answer from the options below:
A 2.8
B 12.5
C 125
D 154
E 375
To determine the work done by the pitcher in accelerating the baseball, we can use the formula:
Work = (1/2) * mass * velocity^2
Given that the mass of the baseball is 250g (or 0.25kg) and the velocity is 50 m/s, we can substitute these values into the formula:
Work = (1/2) * 0.25kg * (50 m/s)^2
= (1/2) * 0.25kg * 2500 m^2/s^2
= 312.5 J
Therefore, the work done by the pitcher is 312.5 Joules.
Since the distance traveled by the baseball is 30 meters, we can use the formula for work done against a force to determine the energy expended:
Energy = work = force * distance
Rearranging the formula, we can solve for force:
force = work / distance = 312.5 J / 30 m = 10.42 N
The energy expended by the pitcher is given by the formula:
Energy = force * distance = 10.42 N * 30 m = 312.5 J
Therefore, the amount of energy expended is 312.5 Joules.
The correct answer is not provided in the options.
To calculate the amount of work done on the baseball, we need to use the formula:
Work = Force x Distance
First, we need to find the force applied to the 250g baseball to make it accelerate to 50 m/s. Newton's second law of motion tells us that the force applied to an object is equal to the mass of the object multiplied by its acceleration:
Force = mass x acceleration
Given that the mass of the baseball is 250g (or 0.25kg) and the acceleration is 50 m/s, we can calculate the force:
Force = 0.25kg x 50 m/s
Force = 12.5 N
Now we can calculate the work done on the baseball over a distance of 30 meters:
Work = Force x Distance
Work = 12.5 N x 30 m
Work = 375 Joules
Therefore, the correct answer is E) 375 Joules.