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A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.?
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A man of mass 50kg is walking on a long wooden board of mass 200kg. th...
Given:
- Mass of the man (m1) = 50 kg
- Mass of the wooden board (m2) = 200 kg
- Velocity of the man relative to the wooden board (v) = 1 m/s
- The wooden board is initially at rest on a frictionless ice surface.
To find:
The velocity of the wooden board after the man starts walking.
Explanation:
1. Conservation of Momentum:
According to the law of conservation of momentum, 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.
The momentum of an object is given by:
Momentum (p) = mass (m) * velocity (v)
2. Initial Momentum:
Before the man starts walking, both the man and the wooden board are at rest. Therefore, the initial momentum of the system is zero.
3. Final Momentum:
After the man starts walking, he imparts a forward momentum to the wooden board.
- The momentum of the man (p1) = mass of the man (m1) * velocity of the man (v)
- The momentum of the wooden board (p2) = mass of the wooden board (m2) * velocity of the wooden board (v2)
Since the man and the wooden board are on a frictionless surface and there are no external forces, their momenta are conserved.
Therefore, the final momentum of the system is equal to the initial momentum, which is zero.
Mathematically,
4. Final Velocity:
The negative sign in the final velocity indicates that the wooden board moves in the opposite direction to the man's velocity relative to the board.
Therefore, the velocity of the wooden board is -0.25 m/s (in the negative x direction) relative to the ice surface.
Answer:
The velocity of the wooden board is -0.25 m/s in the negative x direction relative to the ice surface.
- Mass of the man (m1) = 50 kg
- Mass of the wooden board (m2) = 200 kg
- Velocity of the man relative to the wooden board (v) = 1 m/s
- The wooden board is initially at rest on a frictionless ice surface.
To find:
The velocity of the wooden board after the man starts walking.
Explanation:
1. Conservation of Momentum:
According to the law of conservation of momentum, 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.
The momentum of an object is given by:
Momentum (p) = mass (m) * velocity (v)
2. Initial Momentum:
Before the man starts walking, both the man and the wooden board are at rest. Therefore, the initial momentum of the system is zero.
3. Final Momentum:
After the man starts walking, he imparts a forward momentum to the wooden board.
- The momentum of the man (p1) = mass of the man (m1) * velocity of the man (v)
- The momentum of the wooden board (p2) = mass of the wooden board (m2) * velocity of the wooden board (v2)
Since the man and the wooden board are on a frictionless surface and there are no external forces, their momenta are conserved.
Therefore, the final momentum of the system is equal to the initial momentum, which is zero.
Mathematically,
- Initial momentum = Final momentum
- p1 + p2 = 0
- m1 * v + m2 * v2 = 0
- 50 kg * 1 m/s + 200 kg * v2 = 0
- 50 kg + 200 kg * v2 = 0
- v2 = -50 kg / 200 kg
4. Final Velocity:
The negative sign in the final velocity indicates that the wooden board moves in the opposite direction to the man's velocity relative to the board.
Therefore, the velocity of the wooden board is -0.25 m/s (in the negative x direction) relative to the ice surface.
Answer:
The velocity of the wooden board is -0.25 m/s in the negative x direction relative to the ice surface.
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A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.?
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A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.?.
A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.?.
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A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.?, a detailed solution for A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? has been provided alongside types of A man of mass 50kg is walking on a long wooden board of mass 200kg. the wooden board is initially at rest on a frictionless ice surface. of the man walks with a velocity of v=1m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. velocity is positive in the x direction.? theory, EduRev gives you an
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