A baseball has a mass of .145 kilograms. A pitcher's fastball travels at 42 m/s. How much force is applied to the ball if the catcher stops the ball in .05 sec?
To calculate the force applied to the ball, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a).
Given:
Mass of the baseball, m = 0.145 kg
Final velocity, vf = 0 m/s (since the ball is stopped)
Initial velocity, vi = 42 m/s
Time taken, t = 0.05 s
First, we need to find the acceleration of the ball using the formula for average acceleration:
a = (vf - vi) / t
Substituting the given values:
a = (0 - 42) / 0.05
Simplifying the equation:
a = -42 / 0.05
a = -840 m/s² (Note: The negative sign indicates deceleration)
Now, we can calculate the force using Newton's second law:
F = m * a
Substituting the given mass and acceleration:
F = 0.145 kg * (-840 m/s²)
F = -123 N
The force applied to the ball is approximately -123 Newtons. The negative sign indicates that the force acts in the opposite direction of the initial motion (deceleration).
To calculate the force applied to the ball, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a).
First, let's calculate the acceleration of the ball. Since the pitcher's fastball is stopped by the catcher, we can assume that the final velocity (vf) is 0 m/s. The initial velocity (vi) is given as 42 m/s, and the time taken (t) is 0.05 sec.
We can use the equation:
vf = vi + at
Since final velocity (vf) is 0, and initial velocity (vi) is 42 m/s, we can rearrange the equation to solve for acceleration (a):
a = (vf - vi) / t
a = (0 - 42) / 0.05
Now, let's calculate the acceleration:
a = -42 / 0.05
a = -840 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity. This means that the ball is decelerating.
Next, we can calculate the force applied to the ball by multiplying the mass of the ball (m) by the acceleration (a):
F = m * a
F = 0.145 kg * (-840 m/s^2)
Finally, let's calculate the force:
F = -123.48 N
The force applied to the ball when the catcher stops it is approximately -123.48 Newtons. The negative sign indicates that the force is in the opposite direction of the initial motion.
a = (Vf - Vo) / t,
a = (0 - 42) / 0.05 = -840m/s^2.
F = ma = 0.145 * (-840) = -122N.