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=change in momentum/time

time=(mass * velocity)-(0)/220 N
t=(0.55 kg*3.2)/220N
=0.008 s

To find the duration of the mallet's contact with the ball, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.

The impulse (J) is defined as the product of force (F) and the time interval (Δt) over which the force is applied:

J = F * Δt

The impulse can also be expressed as the change in momentum (Δp) of the ball:

J = Δp

The momentum (p) of an object is defined as the product of its mass (m) and velocity (v):

p = m * v

Therefore, the change in momentum (Δp) can be expressed as:

Δp = m * v - 0

Since the ball is initially at rest, its initial momentum is zero.

Substituting the expression for impulse (J) and change in momentum (Δp) into the equation, we get:

F * Δt = m * v

Rearranging the equation to find the time interval (Δt), we have:

Δt = (m * v) / F

Substituting the given values, we get:

Δt = (0.55 kg * 3.2 m/s) / 220 N

Calculating the value, we find:

Δt = 0.008 s

Therefore, the mallet was in contact with the ball for 0.008 seconds.

To find the time the mallet was in contact with the ball, we can use the concept of impulse. The impulse-momentum theorem states that the impulse acting on an object is equal to the change in momentum of that object. Mathematically, it can be written as:

Impulse = Change in momentum

Impulse (I) is the product of force (F) and time (Δt) and is given by:

I = F * Δt

Momentum (p) is the product of mass (m) and velocity (v) and is given by:

p = m * v

Since the ball is initially at rest, the initial momentum (pinitial) is zero. After being struck, the ball's final momentum (pfinal) is given by:

pfinal = m * v

The change in momentum (Δp) is then:

Δp = pfinal - pinitial = m * v - 0 = m * v

Using the impulse-momentum theorem, we can equate the impulse with the change in momentum:

I = Δp
F * Δt = m * v

Rearranging the equation to solve for time (Δt):

Δt = (m * v) / F

Now we can substitute the given values into the equation to find the time the mallet was in contact with the ball.

Given:
m (mass of the ball) = 0.55 kg
v (speed of the ball) = 3.2 m/s
F (force exerted on the ball) = 220 N

Substituting the values:

Δt = (0.55 kg * 3.2 m/s) / 220 N

Simplifying:

Δt = 9.36 x 10^-3 s

Therefore, the time the mallet was in contact with the ball is approximately 9.36 milliseconds.