An ice hockey puck slides along the ice at 12 m/s. A hockey stick delivers an impulse of 4.0 kg*m/s causing the puck to move off in the opposite direction with the same speed. What is the mass of the puck?
I tried all sorts of ways to set this up and I just cant seem to get it, help?
The momentum change = 2*M*12 m/s = 24 M m/s
where m is the puck mass in kg
That equals the impulse, 4.0 kg m/s
M = 4.0/24 kg = 1/6 kg
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before the impulse is equal to the total momentum after the impulse.
The momentum of an object can be calculated by multiplying its mass by its velocity. Let's assume the mass of the puck is 'm' kg.
Before the impulse:
The momentum of the puck is given by: momentum = mass * velocity
Therefore, the momentum before the impulse is: momentum_before = m * (-12) kg*m/s (since the direction is opposite)
After the impulse:
The momentum after the impulse is given by: momentum_after = m * 12 kg*m/s
According to the principle of conservation of momentum, we can set up the equation:
momentum_before = momentum_after
Which gives us: -12m = 12m
Now, we can solve for the mass of the puck:
-12m = 12m
-12m - 12m = 0
-24m = 0
m = 0 kg
Based on the equation, we found that the mass of the puck is 0 kg. However, this result seems to be invalid since an ice hockey puck must have mass in reality. Therefore, there may be an error in the question or given information.
I would recommend double-checking the numbers or providing additional information if available.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces act on the system.
Let's define the initial direction of the puck's motion as positive (to the right) and the opposite direction as negative (to the left).
The initial momentum of the puck before the impact is given by the product of its mass and velocity: P_initial = m * v_initial.
The final momentum of the puck after the impact is also given by the product of its mass and velocity: P_final = m * v_final.
Since the puck moves off in the opposite direction with the same speed, the final velocity (v_final) is equal to the initial velocity (v_initial), but with the opposite sign.
Using the given values, we have the initial momentum as P_initial = m * (12 m/s). After the impact, the final momentum is P_final = m * (-12 m/s). The impulse delivered by the hockey stick is equal to the change in momentum, which is the difference between the final and initial momentum: Impulse = P_final - P_initial.
Given that the impulse is 4.0 kg*m/s, we can write the equation as follows:
Impulse = P_final - P_initial
4.0 kg*m/s = (m * (-12 m/s)) - (m * (12 m/s))
To solve for the mass (m), let's first distribute the m factor:
4.0 kg*m/s = -12m^2/s - 12m^2/s
Combining like terms:
4.0 kg*m/s = -24m^2/s
Now, let's solve for m by isolating it:
4.0 kg*m/s = -24m^2/s
4.0 kg = -24m
m = -4.0 kg / -24
m = 0.1667 kg
Therefore, the mass of the puck is approximately 0.1667 kg.