Question
A hockey puck with a mass of 0.18 kg travels at a velocity of 40 m/s toward a goalkeeper. The goalkeeper has a mass of 120 kg and is at rest. Assuming a closed system, find the total momentum of the puck before the puck is caught by the goalkeeper. (1 point)
Responses
7.2 kg.m/s
7.2 kg.m/s
-5.3 kg.m/s
-5.3 kg.m/s
0 kg.m/s
0 kg.m/s
6.4 kg.m/s
6.4 kg.m/s
Question 2
A hockey puck with a mass of 0.18 kg travels at a velocity of 40 m/s toward a goalkeeper. The goalkeeper has a mass of 120 kg and is at rest. Assuming a closed system, find the total momentum of the goalkeeper and puck after the puck is caught by the goalkeeper.(1 point)
Responses
7.2 kg.m/s
7.2 kg.m/s
6.4 kg.m/s
6.4 kg.m/s
5.3 kg.m/s
5.3 kg.m/s
4,807 kg.m/s
4,807 kg.m/s
Question 3
What object has the greater momentum after the puck is caught? (1 point)
Responses
The net.
The net.
The goalkeeper
The goalkeeper
The hockey puck
The hockey puck
The ice
The ice
Question 4
What is your justification for choosing the item you did as having the greater momentum?(1 point)
Responses
Momentum is mass times velocity so the momentum would stay inside the hockey puck after it is caught.
Momentum is mass times velocity so the momentum would stay inside the hockey puck after it is caught.
Momentum is absorbed by the net as the puck gets close to it.
Momentum is absorbed by the net as the puck gets close to it.
Momentum is mass times velocity so the greater mass would contain more of the momentum.
Momentum is mass times velocity so the greater mass would contain more of the momentum.
Momentum is absorbed by the ice and is not transferred after it is completely absorbed.
Responses
7.2 kg.m/s
7.2 kg.m/s
-5.3 kg.m/s
-5.3 kg.m/s
0 kg.m/s
0 kg.m/s
6.4 kg.m/s
6.4 kg.m/s
Question 2
A hockey puck with a mass of 0.18 kg travels at a velocity of 40 m/s toward a goalkeeper. The goalkeeper has a mass of 120 kg and is at rest. Assuming a closed system, find the total momentum of the goalkeeper and puck after the puck is caught by the goalkeeper.(1 point)
Responses
7.2 kg.m/s
7.2 kg.m/s
6.4 kg.m/s
6.4 kg.m/s
5.3 kg.m/s
5.3 kg.m/s
4,807 kg.m/s
4,807 kg.m/s
Question 3
What object has the greater momentum after the puck is caught? (1 point)
Responses
The net.
The net.
The goalkeeper
The goalkeeper
The hockey puck
The hockey puck
The ice
The ice
Question 4
What is your justification for choosing the item you did as having the greater momentum?(1 point)
Responses
Momentum is mass times velocity so the momentum would stay inside the hockey puck after it is caught.
Momentum is mass times velocity so the momentum would stay inside the hockey puck after it is caught.
Momentum is absorbed by the net as the puck gets close to it.
Momentum is absorbed by the net as the puck gets close to it.
Momentum is mass times velocity so the greater mass would contain more of the momentum.
Momentum is mass times velocity so the greater mass would contain more of the momentum.
Momentum is absorbed by the ice and is not transferred after it is completely absorbed.
Answers
GPT-4o mini
To answer your questions step by step, let's first calculate the total momentum of the puck before it is caught by the goalkeeper:
### Question 1
**Find the total momentum of the puck before the puck is caught by the goalkeeper.**
The formula for momentum (p) is given by:
\[ p = m \times v \]
where
- \( m \) is the mass,
- \( v \) is the velocity.
For the hockey puck:
- Mass (\( m \)) = 0.18 kg
- Velocity (\( v \)) = 40 m/s
Calculating the momentum:
\[ p_\text{puck} = 0.18 \, \text{kg} \times 40 \, \text{m/s} = 7.2 \, \text{kg.m/s} \]
The total momentum of the puck before being caught is **7.2 kg.m/s.**
**Answer for Question 1:** **7.2 kg.m/s**
---
### Question 2
**Find the total momentum of the goalkeeper and puck after the puck is caught by the goalkeeper.**
Since momentum is conserved in a closed system:
1. Before the catch, we have:
- Momentum of the puck: **7.2 kg.m/s**
- Momentum of the goalkeeper: **0 kg.m/s** (since he is at rest)
Now, the total initial momentum in the system (puck + goalkeeper) before the catch is **7.2 kg.m/s + 0 kg.m/s = 7.2 kg.m/s**.
2. After the puck is caught, the puck and the goalkeeper move together.
- Mass of the puck + mass of the goalkeeper = \( 0.18 \, \text{kg} + 120 \, \text{kg} = 120.18 \, \text{kg} \)
To find the velocity (\( v_f \)) of the combined mass after the catch, we use the equation for momentum conservation:
\[ \text{Total initial momentum} = \text{Total final momentum} \]
\[ 7.2 \, \text{kg.m/s} = (120.18 \, \text{kg}) \times v_f \]
Solving for \( v_f \):
\[ v_f = \frac{7.2 \, \text{kg.m/s}}{120.18 \, \text{kg}} \approx 0.0599 \, \text{m/s} \]
Since we also want to simply state the final momentum of the combined system formed by the puck and the goalkeeper:
Total momentum after the puck is caught remains as **7.2 kg.m/s.**
**Answer 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 puck and the goalkeeper move together as a single system with the total momentum calculated to be 7.2 kg.m/s.
The only relevant objects in this context after the catch are the goalkeeper + puck system, the net, the ice, and the puck itself, but since the puck has come to rest in the goalie's possession, only the goalkeeper + puck has momentum. Thus, when considering momentum:
**Answer for Question 3:** **The goalkeeper**
---
### Question 4
**What is your justification for choosing the item you did as having the greater momentum?**
Since the momentum of a system is the sum of its components, the goalkeeper now moving with the puck has the combined system mass and its respective momentum. The net, ice, and puck do not exhibit more momentum than the goalkeeper after the puck is caught.
The best explanation here is:
**Answer for Question 4:** **Momentum is mass times velocity so the greater mass would contain more of the momentum.**
### Question 1
**Find the total momentum of the puck before the puck is caught by the goalkeeper.**
The formula for momentum (p) is given by:
\[ p = m \times v \]
where
- \( m \) is the mass,
- \( v \) is the velocity.
For the hockey puck:
- Mass (\( m \)) = 0.18 kg
- Velocity (\( v \)) = 40 m/s
Calculating the momentum:
\[ p_\text{puck} = 0.18 \, \text{kg} \times 40 \, \text{m/s} = 7.2 \, \text{kg.m/s} \]
The total momentum of the puck before being caught is **7.2 kg.m/s.**
**Answer for Question 1:** **7.2 kg.m/s**
---
### Question 2
**Find the total momentum of the goalkeeper and puck after the puck is caught by the goalkeeper.**
Since momentum is conserved in a closed system:
1. Before the catch, we have:
- Momentum of the puck: **7.2 kg.m/s**
- Momentum of the goalkeeper: **0 kg.m/s** (since he is at rest)
Now, the total initial momentum in the system (puck + goalkeeper) before the catch is **7.2 kg.m/s + 0 kg.m/s = 7.2 kg.m/s**.
2. After the puck is caught, the puck and the goalkeeper move together.
- Mass of the puck + mass of the goalkeeper = \( 0.18 \, \text{kg} + 120 \, \text{kg} = 120.18 \, \text{kg} \)
To find the velocity (\( v_f \)) of the combined mass after the catch, we use the equation for momentum conservation:
\[ \text{Total initial momentum} = \text{Total final momentum} \]
\[ 7.2 \, \text{kg.m/s} = (120.18 \, \text{kg}) \times v_f \]
Solving for \( v_f \):
\[ v_f = \frac{7.2 \, \text{kg.m/s}}{120.18 \, \text{kg}} \approx 0.0599 \, \text{m/s} \]
Since we also want to simply state the final momentum of the combined system formed by the puck and the goalkeeper:
Total momentum after the puck is caught remains as **7.2 kg.m/s.**
**Answer 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 puck and the goalkeeper move together as a single system with the total momentum calculated to be 7.2 kg.m/s.
The only relevant objects in this context after the catch are the goalkeeper + puck system, the net, the ice, and the puck itself, but since the puck has come to rest in the goalie's possession, only the goalkeeper + puck has momentum. Thus, when considering momentum:
**Answer for Question 3:** **The goalkeeper**
---
### Question 4
**What is your justification for choosing the item you did as having the greater momentum?**
Since the momentum of a system is the sum of its components, the goalkeeper now moving with the puck has the combined system mass and its respective momentum. The net, ice, and puck do not exhibit more momentum than the goalkeeper after the puck is caught.
The best explanation here is:
**Answer for Question 4:** **Momentum is mass times velocity so the greater mass would contain more of the momentum.**