A 45.4-kg girl is standing on a 149-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.52î m/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface? -0.7 Your response differs from the correct answer by more than 10%. Double check your calculations.i m/s (b) What is the girl's velocity relative to the ice surface? 1.2 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.î m/s
A 45.4-kg girl is standing on a 149-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.52î m/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface? -0.7 Your response differs from the correct answer by more than 10%. Double check your calculations.i m/s (b) What is the girl's velocity relative to the ice surface? 1.2 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.î m/s
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
A 45.4-kg girl is standing on a 149-kg plank. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.52 m/s relative to the plank.
**Questions:**
(a) What is the velocity of the plank relative to the ice surface?
- User's Response: 0.7 m/s ❌
- Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations.
(b) What is the girl's velocity relative to the ice surface?
- User's Response: 1.2 m/s ❌
- Feedback: Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.
**Explanation:**
In this problem, we are observing a classic example of the conservation of momentum on a frictionless surface. Since there are no external forces acting horizontally, the total momentum of the system (girl + plank) remains constant.
1. When the girl walks on the plank:
- She moves forward, exerting a force backward on the plank.
- The plank, in turn, moves backward, equalizing the momentum exchange as they are isolated on the frictionless surface.
The calculations for such a problem typically involve using the formulas for center of mass and conservation of momentum:
- Let \( v_g \) be the girl’s velocity relative to the ice, and \( v_p \) be the plank's velocity relative to the ice.
The conservation of momentum equation is:
\[ (m_{\text{girl}} \cdot v_g) + (m_{\text{plank}} \cdot v_p) = 0 \]
Where:
- \( m_{\text{girl}} = 45.4 \, \text{kg} \)
- \( m_{\text{plank}} = 149 \, \text{kg} \)
Substitute:
\[ (45.4 \cdot (1.52 + v_p)) + (149 \cdot v_p) = 0 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbab9b6c1-a299-4916-ab03-e898a054c7d5%2F08d962b3-903c-48ed-9f5b-82a086a4946b%2Fnfnly2q_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 45.4-kg girl is standing on a 149-kg plank. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.52 m/s relative to the plank.
**Questions:**
(a) What is the velocity of the plank relative to the ice surface?
- User's Response: 0.7 m/s ❌
- Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations.
(b) What is the girl's velocity relative to the ice surface?
- User's Response: 1.2 m/s ❌
- Feedback: Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.
**Explanation:**
In this problem, we are observing a classic example of the conservation of momentum on a frictionless surface. Since there are no external forces acting horizontally, the total momentum of the system (girl + plank) remains constant.
1. When the girl walks on the plank:
- She moves forward, exerting a force backward on the plank.
- The plank, in turn, moves backward, equalizing the momentum exchange as they are isolated on the frictionless surface.
The calculations for such a problem typically involve using the formulas for center of mass and conservation of momentum:
- Let \( v_g \) be the girl’s velocity relative to the ice, and \( v_p \) be the plank's velocity relative to the ice.
The conservation of momentum equation is:
\[ (m_{\text{girl}} \cdot v_g) + (m_{\text{plank}} \cdot v_p) = 0 \]
Where:
- \( m_{\text{girl}} = 45.4 \, \text{kg} \)
- \( m_{\text{plank}} = 149 \, \text{kg} \)
Substitute:
\[ (45.4 \cdot (1.52 + v_p)) + (149 \cdot v_p) = 0 \]
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