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?
The work done on an object can be calculated using the equation W = F * d * cos(theta), where W is the work done, F is the force applied, d is the distance traveled, and theta is the angle between the applied force and the direction of motion.
In this case, we need to determine the force applied to the baseball in order to accelerate it to 50 m/s. We can use Newton's second law, F = ma, where m is the mass of the baseball and a is the acceleration.
Given that the baseball has a mass of 250g (or 0.25kg) and accelerates to 50 m/s, the force applied can be calculated as F = 0.25kg * 50m/s^2 = 12.5 N.
The work done on the baseball in traveling a distance of 30 meters can now be calculated as W = F * d * cos(theta). Since the angle between the applied force and the direction of motion is generally assumed to be zero, cos(theta) = 1.
Therefore, W = 12.5 N * 30 m * 1 = 375 J.
The amount of energy (in Joules) expended or work done on the baseball is 375 J.
To calculate the work done, we need to use the equation:
Work = Force × Distance
First, let's find the force applied to accelerate the baseball. We can use Newton's second law:
Force = Mass × Acceleration
The mass of the baseball is given as 250 grams. To convert it to kilograms, we divide by 1000:
Mass = 250 g / 1000 = 0.25 kg
The acceleration is given as 50 m/s. Now we can calculate the force:
Force = 0.25 kg × 50 m/s = 12.5 N
Next, we need to calculate the work done for the baseball to travel a distance of 30 meters:
Work = Force × Distance = 12.5 N × 30 m = 375 J
Therefore, the work done (energy expended) is 375 Joules.