Let's go through each question step-by-step.
Question 1: Find the total momentum of the puck before it is caught by the goalkeeper.
The momentum \( p \) of an object is calculated using the formula:
\[ p = m \times v \]
Where:
- \( m \) is the mass of the object (in kg)
- \( v \) is the velocity of the object (in m/s)
For the hockey puck:
- Mass \( m = 0.18 , \text{kg} \)
- Velocity \( v = 40 , \text{m/s} \)
So the momentum of the puck is:
\[ p_{\text{puck}} = 0.18 , \text{kg} \times 40 , \text{m/s} = 7.2 , \text{kg.m/s} \]
Since the goalkeeper is at rest, his momentum is 0. Thus, the total momentum before the puck is caught is:
\[ p_{\text{total, before}} = p_{\text{puck}} + p_{\text{goalkeeper}} = 7.2 , \text{kg.m/s} + 0 = 7.2 , \text{kg.m/s} \]
Response for Question 1:
- 7.2 kg.m/s
Question 2: Find the total momentum of the goalkeeper and puck after the puck is caught.
When the puck is caught by the goalkeeper, they will move together. Therefore, we calculate the total momentum after the catch using conservation of momentum.
The total mass after the puck is caught will be:
- Mass of puck = 0.18 kg
- Mass of goalkeeper = 120 kg
Total mass = \( 0.18 + 120 = 120.18 , \text{kg} \)
Using conservation of momentum (initial momentum = final momentum):
Initial momentum before the catch = \( 7.2 , \text{kg.m/s} \)
After the puck is caught, the velocity \( v_f \) can be found using:
\[ p_{\text{total, before}} = p_{\text{total, after}} \]
Let’s denote the combined velocity of the puck and goalkeeper after the catch as \( v_f \):
\[ 7.2 , \text{kg.m/s} = 120.18 , \text{kg} \times v_f \]
Solving for \( v_f \):
\[ v_f = \frac{7.2 , \text{kg.m/s}}{120.18 , \text{kg}} \approx 0.0599 , \text{m/s} \]
Now, the total momentum of the goalkeeper and puck after the puck is caught is:
\[ p_{\text{total, after}} = 120.18 , \text{kg} \times 0.0599 , \text{m/s} \approx 7.2 , \text{kg.m/s} \]
Response for Question 2:
- 7.2 kg.m/s
Question 3: What object has the greater momentum after the puck is caught?
After the puck is caught, the total momentum is conserved. Therefore, the combined momentum of the goalkeeper and the puck remains 7.2 kg.m/s. Since momentum is conserved, the goalkeeper and puck together have the same momentum as the puck alone before the catch.
Response for Question 3:
- The goalkeeper
Question 4: What is your justification for choosing the item you did as having the greater momentum?
The justification involves an understanding of the principle of momentum conservation:
Momentum is also conserved during the catch, meaning that the total momentum of the goalie and puck system does not change from the initial momentum of the puck. The goalkeeper, having caught the puck, now possesses a momentum that results from both their mass and the velocity gained after the catch.
Response for Question 4:
- Momentum is mass times velocity so the greater mass would contain more of the momentum.
This choice reflects the conservation of momentum in the system. However, it must be noted that the total momentum remains consistent; hence the addition of the puck grants the goalkeeper together with the puck an identical momentum as what the puck had before.