A 0.55-{kg} croquet ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 220 N. If the ball's speed after being struck is 3.2 m/s, how long was the mallet in contact with the ball?
force * time = change in momentum
time = m v/220 = .55*3.2 / 220
To find the time the mallet was in contact with the ball, we can use the impulse-momentum principle. The impulse (change in momentum) is equal to the average force applied multiplied by the time interval over which the force was applied.
1. First, calculate the change in momentum of the ball. The momentum of an object is given by the formula: momentum = mass * velocity. In this case, the object is the croquet ball.
Momentum before being struck = 0 (since the ball is initially at rest)
Momentum after being struck = mass * final velocity
Momentum after being struck = (0.55 kg) * (3.2 m/s)
2. Calculate the change in momentum by finding the difference between the momentum before being struck and the momentum after being struck.
Change in momentum = Momentum after being struck - Momentum before being struck
3. Now, use the impulse-momentum principle equation to solve for the time interval.
Impulse = average force * time interval
Rearranging the formula, we get:
Time interval = Impulse / average force
4. Substitute the values into the equation. The impulse is equal to the change in momentum from step 2, and the average force is given as 220 N.
Time interval = (change in momentum) / average force
5. Calculate and substitute the values to find the time interval.
Time interval = ((0.55 kg) * (3.2 m/s)) / 220 N
Time interval ≈ 0.008 s
Therefore, the mallet was in contact with the ball for approximately 0.008 seconds.