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Chapter 15: Problem 5

A hockey puck is traveling to the left with a velocity of \(v_{1}=10 \mathrm{~m} / \mathrm{s}\) when it is struck by a hockey stick and given a velocity of \(v_{2}=20 \mathrm{~m} / \mathrm{s}\) as shown. Determine the magnitude of the net impulse exerted by the hockey stick on the puck. The puck has a mass of \(0.2 \mathrm{~kg}\).

Short Answer

Expert verified
The magnitude of the net impulse exerted by the hockey stick on the puck is \(2 \, kg \cdot m/s\) to the left.

Step by step solution

01

Determine the initial and final velocities

The initial velocity of the hockey puck is given as \(v_{1}=10 \, m/s\) to the left. After being hit by the hockey stick, the final velocity changed to \(v_{2}=20 \, m/s\) to the left. It is important to note the directions here, as the direction will affect the sign of the velocities.
02

Determine the mass of the puck

The mass of the puck is given as \(0.2 \, kg\). This value will be used to calculate the momentum of the puck before and after being hit by the hockey stick.
03

Calculate the initial and final momentums

To calculate initial and final momentums, multiply the mass of the object by its initial and final velocities respectively. Therefore, Initial momentum = \(v_{1} \times mass = 10 \times 0.2 = 2 \, kg \cdot m/s\) to the left and Final momentum = \(v_{2} \times mass = 20 \times 0.2 = 4 \, kg \cdot m/s\) to the left.
04

Calculate the net impulse

By definition, impulse is the change in momentum. So, to get the impulse, subtract the initial momentum from the final momentum: Impulse = Final momentum - Initial momentum = \(4 \, kg \cdot m/s - 2 \, kg \cdot m/s = 2 \, kg \cdot m/s\) to the left. The direction has been mentioned to clarify that the impulse is exerted in the same direction as the velocity, which is the left direction in this case.

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Most popular questions from this chapter

A snowblower having a scoop \(S\) with a crosssectional area of \(A_{\mathrm{s}}=0.12 \mathrm{~m}^{3}\) is pushed into snow with a speed of \(v_{s}=0.5 \mathrm{~m} / \mathrm{s}\). The machine discharges the snow through a tube \(T\) that has a cross-sectional area of \(A_{T}=0.03 \mathrm{~m}^{2}\) and is directed \(60^{\circ}\) from the horizontal. If the density of snow is \(\rho_{s}=104 \mathrm{~kg} / \mathrm{m}^{3}\), determine the horizontal force \(P\) required to push the blower forward, and the resultant frictional force \(F\) of the wheels on the ground, necessary to prevent the blower from moving sideways. The wheels roll freely.

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