A man swings a 1.25 kg bat. He swings it at 42.0 m/s with a force of 272 N, which brings the bat to rest after it hits its target. How long was the bottle in contact with the target?
force * time = change of momentum = original m*v
V = Vo +
To determine the time the bat was in contact with the target, we can use the equation of motion:
Force (F) = Mass (m) × Acceleration (a)
In this case, the force applied by the man swinging the bat (272 N) causes the bat to decelerate until it comes to rest. Therefore, the acceleration (a) will be negative.
Using the equation for acceleration:
a = Δv / Δt
where Δv is the change in velocity and Δt is the change in time, we can rewrite the equation as:
F = m × (Δv / Δt)
Rearranging the equation, we get:
Δt = m × Δv / F
Given the mass of the bat (m = 1.25 kg) and the force applied (F = 272 N), we need to find the change in velocity (Δv) to calculate the time.
The initial velocity (u) of the bat is 42.0 m/s, and the final velocity (v) is 0 m/s since the bat comes to rest.
Using the equation for change in velocity:
Δv = v - u
Δv = 0 m/s - 42.0 m/s
Δv = -42.0 m/s
Now we can substitute the values into the equation for Δt:
Δt = (1.25 kg) × (-42.0 m/s) / (272 N)
Calculating this equation will give us the time the bat was in contact with the target.