A 0.4 kg hockey puck moving at 30 m/s hits

a straw bale, stopping in 1.4 s.
What impulse was imparted to the hockey
puck?

To find the impulse imparted to the hockey puck, we can use the equation:

Impulse = Change in momentum

The momentum of an object is given by the equation:

Momentum = mass × velocity

Given:
Mass of the hockey puck (m) = 0.4 kg
Initial velocity of the hockey puck (u) = 30 m/s
Final velocity of the hockey puck (v) = 0 m/s (as it stops)
Time taken to stop (t) = 1.4 s

Step 1: Calculate the change in velocity:
Change in velocity (Δv) = Final velocity (v) - Initial velocity (u)
Δv = 0 m/s - 30 m/s
Δv = -30 m/s

Step 2: Calculate the change in momentum:
Change in momentum (Δp) = Mass (m) × Change in velocity (Δv)
Δp = 0.4 kg × (-30 m/s)
Δp = -12 kg⋅m/s

The magnitude of the impulse imparted to the hockey puck is 12 kg⋅m/s.

To find the impulse imparted to the hockey puck, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in its momentum.

The formula for impulse can be written as:

Impulse = force x time

In this case, since the hockey puck stopped, we can assume that the net force acting on it is equal to zero. Therefore, the impulse can be calculated by finding the change in momentum of the hockey puck.

The formula for momentum is:

Momentum = mass x velocity

Given:
Mass of the hockey puck (m) = 0.4 kg
Initial velocity of the hockey puck (u) = 30 m/s
Final velocity of the hockey puck (v) = 0 m/s
Time taken for the hockey puck to stop (t) = 1.4 s

First, calculate the initial momentum of the hockey puck:

Initial momentum (Mu) = mass x initial velocity
= m x u

Next, calculate the final momentum of the hockey puck:

Final momentum (Mv) = mass x final velocity
= m x v

Since the hockey puck stopped, its final velocity is 0 m/s.

Now, calculate the change in momentum:

Change in momentum (ΔM) = Final momentum - Initial momentum
= Mv - Mu

Substitute the values:

ΔM = (m x v) - (m x u)

Finally, calculate the impulse:

Impulse = Force x time

Since the net force is zero, impulse is equal to the change in momentum:

Impulse = ΔM

Now, let's substitute the known values into the equation to find the impulse.

Mass * Velocity / Time