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A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.?
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A block of mass 'm' slides without friction down a fixed inclined boar...
If it is on the surface of our planet, there will be a downward force equivalent to an acceleration of 32 feet per second pers second. The slope will have a movement along the surface that is equal to two feet for each foot of downward movement. This reduces the acceleration by a factor of two. This is because 60 degrees is a triangle of three equal sides. 30 degrees is half a side so the slope is twice the length of the drop.
The block will have a force that will accelerate 16 feet per second per second.
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A block of mass 'm' slides without friction down a fixed inclined boar...
Analysis:
To find the velocity of the cart when the block drops on it, we need to consider the conservation of energy and momentum.
Conservation of Energy:
When the block slides down the inclined board, it gains potential energy due to its initial height h. As it reaches the bottom of the incline, all the potential energy is converted into kinetic energy.
The potential energy of the block at height h is given by:
Potential Energy = mgh
At the bottom of the incline, the potential energy is converted into kinetic energy:
Kinetic Energy = (1/2)mv^2
Since there is no friction, the kinetic energy gained by the block is equal to the kinetic energy of the cart when the block drops on it.
Conservation of Momentum:
When the block drops on the cart, the momentum of the system is conserved. The momentum of the block just before it drops is given by:
Momentum of the block = m * velocity of the block
The momentum of the cart just after the block drops on it is given by:
Momentum of the cart = M * velocity of the cart
Since momentum is conserved, we can equate the momentum of the block and the cart:
m * velocity of the block = M * velocity of the cart
Combining the Equations:
Equating the kinetic energy gained by the block and the kinetic energy of the cart, we have:
(1/2)mv^2 = (1/2)MV^2
Simplifying the equation, we get:
v^2 = (M/m) * V^2
Now, substituting the momentum equation into the equation above, we have:
v^2 = (M/m) * (m * velocity of the block)^2
Simplifying further, we get:
v^2 = M * (velocity of the block)^2
Taking the square root of both sides, we have:
v = √(M * (velocity of the block)^2)
Therefore, the velocity of the cart when the block drops on it is equal to the velocity of the block itself, multiplied by the square root of the ratio of masses M/m.
Conclusion:
The velocity of the cart when the block drops on it is determined by the initial velocity of the block sliding down the inclined board and the ratio of masses between the block and the cart. The conservation of energy and momentum principles allow us to derive this relationship.
To find the velocity of the cart when the block drops on it, we need to consider the conservation of energy and momentum.
Conservation of Energy:
When the block slides down the inclined board, it gains potential energy due to its initial height h. As it reaches the bottom of the incline, all the potential energy is converted into kinetic energy.
The potential energy of the block at height h is given by:
Potential Energy = mgh
At the bottom of the incline, the potential energy is converted into kinetic energy:
Kinetic Energy = (1/2)mv^2
Since there is no friction, the kinetic energy gained by the block is equal to the kinetic energy of the cart when the block drops on it.
Conservation of Momentum:
When the block drops on the cart, the momentum of the system is conserved. The momentum of the block just before it drops is given by:
Momentum of the block = m * velocity of the block
The momentum of the cart just after the block drops on it is given by:
Momentum of the cart = M * velocity of the cart
Since momentum is conserved, we can equate the momentum of the block and the cart:
m * velocity of the block = M * velocity of the cart
Combining the Equations:
Equating the kinetic energy gained by the block and the kinetic energy of the cart, we have:
(1/2)mv^2 = (1/2)MV^2
Simplifying the equation, we get:
v^2 = (M/m) * V^2
Now, substituting the momentum equation into the equation above, we have:
v^2 = (M/m) * (m * velocity of the block)^2
Simplifying further, we get:
v^2 = M * (velocity of the block)^2
Taking the square root of both sides, we have:
v = √(M * (velocity of the block)^2)
Therefore, the velocity of the cart when the block drops on it is equal to the velocity of the block itself, multiplied by the square root of the ratio of masses M/m.
Conclusion:
The velocity of the cart when the block drops on it is determined by the initial velocity of the block sliding down the inclined board and the ratio of masses between the block and the cart. The conservation of energy and momentum principles allow us to derive this relationship.
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A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.?
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A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.?.
A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of mass 'm' slides without friction down a fixed inclined board of inclination alpha with the horizontal. After leaving the inclined, the block falls on a cart of mass 'M'. Initial height of the block above the level is h. The velocity of cart when block drops on it will be.?.
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