How much force (in Newtons) does a baseball pitcher have to exert on a 250g baseball to make it accelerate to 50 m/s the instant that it leaves his hand?
To determine the force required, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a).
Given:
Mass of the baseball (m) = 250g = 0.25kg
Final velocity (v) = 50 m/s
Initial velocity (u) = 0 m/s (since the ball starts from rest)
The acceleration (a) can be calculated using the following equation:
v^2 = u^2 + 2as
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Since the baseball pitcher wants the ball to reach 50 m/s at an instant (which means s = 0), we can use the equation to find the acceleration:
a = (50^2 - 0) / (2 * 0) = 0
Thus, the required force on the baseball is zero since there is no acceleration needed to achieve the desired velocity of 50 m/s the instant it leaves the pitcher's hand.
To determine the force exerted by a baseball pitcher to accelerate a 250g baseball to 50 m/s, we can use Newton's second law of motion:
Force (F) = mass (m) x acceleration (a)
Given:
Mass of the baseball (m) = 250 grams = 0.25 kg
Final velocity (v) = 50 m/s
We know that the initial velocity of the baseball is 0 m/s because it is at rest when the pitcher throws it. We also know that the time taken to accelerate to the final velocity is instant, which means there is no time period involved. Assuming there is no air resistance, we can calculate the acceleration using the equation:
v² = u² + 2as,
where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the displacement (which we can assume to be 1 meter since the ball just leaves the hand).
Rearranging the equation to solve for acceleration:
a = (v² - u²) / (2s)
a = (50² - 0²) / (2 x 1)
a = 2500 / 2
a = 1250 m/s²
Now, we can substitute the values into the force equation:
F = m x a
F = 0.25 kg x 1250 m/s²
F = 312.5 Newtons
Therefore, the baseball pitcher needs to exert a force of 312.5 Newtons on the 250g baseball to make it accelerate to 50 m/s the instant it leaves his hand.