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In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are?
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In the arrangement shown in figure the block of mass = 2 kg lies on th...
Problem Statement
A block of mass 2 kg lies on a wedge of mass M = 8 kg. Determine the initial acceleration of the wedge if the surface is frictionless.
Solution
The problem involves the application of Newton's second law of motion and the principle of conservation of energy.
Step 1: Free Body Diagram
Draw the free body diagram of the block and the wedge.
where:
- m = mass of the block (2 kg)
- M = mass of the wedge (8 kg)
- g = acceleration due to gravity (9.8 m/s^2)
- N = normal force
- f = frictional force
- a = acceleration of the system
Step 2: Apply Newton's Second Law
Apply Newton's second law of motion to the block and the wedge.
- Block: m*a = f
- Wedge: (M+m)*a = N - M*g
Step 3: Apply Conservation of Energy
Apply the principle of conservation of energy to the system.
The initial potential energy of the system is:
- PEi = m*g*h
where h is the height of the block above the ground.
The final kinetic energy of the system is:
- KEf = (M+m)*v^2/2
where v is the final velocity of the system.
Since the surface is frictionless, there is no work done by friction, and the total mechanical energy of the system is conserved.
Therefore, the initial potential energy of the system is equal to the final kinetic energy of the system.
- PEi = KEf
- m*g*h = (M+m)*v^2/2
Step 4: Solve for the Acceleration
Substitute the expression for f from the block equation into the wedge equation.
- (M+m)*a = N - M*g
- (M+m)*a = m*g + m*a - M*g
- a = (m-M)*g/(M+m)
Substitute the expression for v^2 from the energy equation into the acceleration equation.
- a = g*(m-M)/(M+m)
Substitute the given values of m and M into the acceleration equation.
- a = g*(2-8)/(2+8)
- a = -6g/10
- a = -0.588 m/s^2
Step 5: Conclusion
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In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are?
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In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are? 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 In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are?.
In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are? 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 In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the arrangement shown in figure the block of mass = 2 kg lies on the wedge of mass M = 8 kg. The initial acceleration of wedge if the surface are?.
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