This came up on our test review for tomorrow, and I'm stumped!
"A hockey puck of mass 0.51 kg is moving north across the ice with a speed of 32 m/s. If it is hit with a hockey stick so as to make it travel due west at the same speed, what is the magnitude of the impulse delivered to the puck?"
My FBD shows the puck bouncing off the stick and heading in a unknown direction at 32 m/s. I found the momentum of the puck to be p=16.32, but I can't seem to calculate the magnitude. Can anyone help me?
Thanks! I had to go through the whole vector diagram, but got it in the end.
To find the magnitude of the impulse delivered to the hockey puck, you can use the principle of conservation of linear momentum.
The initial momentum of the puck is given by its mass (m) multiplied by its initial velocity (v):
Initial momentum = m * v
Since the puck is moving north with a speed of 32 m/s, its initial momentum is:
Initial momentum = 0.51 kg * 32 m/s
Now, when the puck is hit by the hockey stick and starts moving due west, its final momentum is also given by its mass (m) multiplied by its final velocity (v'):
Final momentum = m * v'
Since the puck is now moving due west with a speed of 32 m/s, its final momentum is:
Final momentum = 0.51 kg * 32 m/s
According to the principle of conservation of linear momentum, the initial momentum and the final momentum must be equal.
Therefore, the magnitude of the impulse delivered to the puck is the change in momentum, which can be calculated as the difference between the final momentum and the initial momentum:
Impulse = Final momentum - Initial momentum
Impulse = (0.51 kg * 32 m/s) - (0.51 kg * 32 m/s)
Simplifying this expression, we get:
Impulse = 0 Ns
Therefore, the magnitude of the impulse delivered to the puck is 0 Ns.
To find the magnitude of the impulse delivered to the puck, you need to use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. In this case, the initial momentum of the puck moving north is given by:
p_initial = mass * velocity
= (0.51 kg) * (32 m/s)
= 16.32 kg·m/s
According to the principle of conservation of momentum, the total momentum before and after the hit should remain the same. After the hit, the puck is moving due west.
Now, to find the magnitude of the impulse, we need to calculate the change in momentum. The change in momentum is given by the difference in the initial and final momenta:
Δp = p_final - p_initial
Since the puck ends up moving due west at the same speed, its final momentum would be:
p_final = mass * velocity
= (0.51 kg) * (32 m/s)
= 16.32 kg·m/s
Now let's calculate the change in momentum:
Δp = (16.32 kg·m/s) - (16.32 kg·m/s)
= 0 kg·m/s
The magnitude of the impulse delivered to the puck is equal to the change in momentum, which in this case is zero (Δp = 0 kg·m/s) since the direction changed but the speed remained the same.
So, the magnitude of the impulse delivered to the puck is zero.
There is a change in direction of the momentum by 90 degrees. The magnitude of the momentum remains 16.32 kg m/s.
The magnitude of the impulse equals the magnitude of the momentum change VECTOR. That would be sqrt2 times 16.32 kg m/s
Do you see why? If not, draw yourself the vector diagram