A 0.15 kg baseball moving at +21.20 m/s is slowed to a stop by a catcher who exerts a constant force of -362 N.How long does it take this force to stop the ball?
Question
A 0.15 kg baseball moving at +21.20 m/s is slowed to a stop by a catcher who exerts a constant force of -362 N.How long does it take this force to stop the ball?
Solution 1
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).
First, we need to find the acceleration of the baseball. Since the force and the direction of the motion are opposite, the acceleration is negative. We can find it by rearranging the formula to a = F/m.
a = F/m a = -362 N / 0.15 kg a = -2413.33 m/s²
Next, we use the formula for acceleration, which is a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. We can rearrange this formula to solve for time: Δt = Δv/a.
The change in velocity is the final velocity minus the initial velocity. Since the ball is stopped, the final velocity is 0 m/s. So, Δv = 0 m/s - 21.20 m/s = -21.20 m/s.
Now we can find the time it takes for the force to stop the ball:
Δt = Δv/a Δt = -21.20 m/s / -2413.33 m/s² Δt = 0.00878 s
So, it takes approximately 0.00878 seconds for the force to stop the ball.
Solution 2
To solve this problem, we can use the second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
First, we need to find the acceleration of the baseball. Since the force and the direction of the motion are opposite, the acceleration is negative. We can find it by rearranging the formula to a = F/m.
a = F/m = -362 N / 0.15 kg = -2413.33 m/s²
Next, we use the formula for acceleration, which is a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. We can rearrange this formula to solve for time: Δt = Δv/a.
The change in velocity is the final velocity minus the initial velocity. Since the ball is stopped, the final velocity is 0 m/s. So, Δv = 0 m/s - 21.20 m/s = -21.20 m/s.
Now we can find the time it takes for the force to stop the ball:
Δt = Δv/a = -21.20 m/s / -2413.33 m/s² = 0.00878 s
So, it takes approximately 0.00878 seconds for the catcher's force to stop the ball.
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