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Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A?
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Q9. A object of mass 3 kg slides down an inclined plan and reaches C i...
Problem Overview
An object of mass 3 kg slides down an inclined plane and reaches point C in 1 second. The coefficient of kinetic friction is given as 0.5. We need to find the initial speed of the object when it is released from position A.
Given Data
- Mass (m): 3 kg
- Coefficient of kinetic friction (μ): 0.5
- Time (t): 1 sec
Forces Acting on the Object
- Gravitational Force (Weight) (W): W = m * g, where g = 9.81 m/s².
- Normal Force (N): Acts perpendicular to the inclined plane.
- Frictional Force (F_friction): F_friction = μ * N.
Calculating the Net Force
1. The gravitational force acting down the incline can be calculated as:
- F_gravity = m * g * sin(θ)
2. The normal force is:
- N = m * g * cos(θ)
3. The frictional force:
- F_friction = μ * N = μ * (m * g * cos(θ))
4. The net force (F_net) acting on the object as it moves down the incline:
- F_net = F_gravity - F_friction
Acceleration Calculation
Using Newton's second law:
- F_net = m * a, where a is the acceleration.
The acceleration can be expressed as:
- a = (F_gravity - F_friction) / m
Distance Calculation
Using the kinematic equation:
- Distance (s) = initial velocity (u) * t + 0.5 * a * t²
- Given that distance is unknown, we rearrange to find initial velocity (u).
Conclusion
To find the initial speed of the object, we need to calculate the net forces, determine the resulting acceleration, and use the kinematic equations to solve for the initial speed. The calculations involve substituting the values and solving the equations systematically.
An object of mass 3 kg slides down an inclined plane and reaches point C in 1 second. The coefficient of kinetic friction is given as 0.5. We need to find the initial speed of the object when it is released from position A.
Given Data
- Mass (m): 3 kg
- Coefficient of kinetic friction (μ): 0.5
- Time (t): 1 sec
Forces Acting on the Object
- Gravitational Force (Weight) (W): W = m * g, where g = 9.81 m/s².
- Normal Force (N): Acts perpendicular to the inclined plane.
- Frictional Force (F_friction): F_friction = μ * N.
Calculating the Net Force
1. The gravitational force acting down the incline can be calculated as:
- F_gravity = m * g * sin(θ)
2. The normal force is:
- N = m * g * cos(θ)
3. The frictional force:
- F_friction = μ * N = μ * (m * g * cos(θ))
4. The net force (F_net) acting on the object as it moves down the incline:
- F_net = F_gravity - F_friction
Acceleration Calculation
Using Newton's second law:
- F_net = m * a, where a is the acceleration.
The acceleration can be expressed as:
- a = (F_gravity - F_friction) / m
Distance Calculation
Using the kinematic equation:
- Distance (s) = initial velocity (u) * t + 0.5 * a * t²
- Given that distance is unknown, we rearrange to find initial velocity (u).
Conclusion
To find the initial speed of the object, we need to calculate the net forces, determine the resulting acceleration, and use the kinematic equations to solve for the initial speed. The calculations involve substituting the values and solving the equations systematically.
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Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A?
Question Description
Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A?.
Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q9. A object of mass 3 kg slides down an inclined plan and reaches C in 1 sec . Coefficient of kinetic friction is 0.5 Find the initial speed of the object when it is released from position A?.
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