A ball has a mass of 150 grams and is throw at 105 mph. The ball stops in a catcher mitt in 0.2 seconds. what force is applied to stop this ball? Find this force un newtons and in pounds.
To find the force applied to stop the ball, 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): F = m * a.
First, we need to convert the mass of the ball from grams to kilograms, as the standard unit for mass in the International System of Units (SI) is kilograms. Given that 1 kilogram (kg) is equal to 1000 grams (g), we can convert the mass as follows:
Mass (m) = 150 grams * (1 kilogram / 1000 grams) = 0.15 kilograms
Next, we need to calculate the acceleration. Using the formula for acceleration (a = Δv / Δt), we can find the change in velocity (Δv) by converting the initial velocity from mph (miles per hour) to meters per second (m/s). Given that 1 mile is equal to 1.60934 kilometers and 1 hour is equal to 3600 seconds, we can convert the velocity as follows:
Initial velocity (v) = 105 mph * (1.60934 km / 1 mile) * (1000 m / 1 km) * (1 hour / 3600 seconds) = 47.0244 m/s
The final velocity (vf) is 0 m/s since the ball stops, and the time taken (Δt) is 0.2 seconds. Thus, the change in velocity (Δv) is calculated as follows:
Δv = vf - v = 0 - 47.0244 m/s = -47.0244 m/s
Now we can calculate the acceleration (a) by dividing the change in velocity by the time taken:
a = Δv / Δt = (-47.0244 m/s) / (0.2 seconds) = -235.122 m/s^2
Note: The negative sign indicates deceleration since the ball is stopping.
Finally, we can determine the force (F) applied to stop the ball by multiplying the mass (m) by the acceleration (a):
F = m * a = (0.15 kilograms) * (-235.122 m/s^2) = -35.2683 N
The force applied to stop the ball is approximately -35.2683 Newtons.
To convert this force into pounds, we can use the conversion factor 1 Newton (N) = 0.22481 pounds (lb):
Force in pounds = -35.2683 N * (0.22481 lb / 1 N) = -7.9329 lb
Therefore, the force applied to stop the ball is approximately -35.2683 Newtons (-7.9329 pounds).