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A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²
calculate wd by tension?
calculate wd by tension?
Most Upvoted Answer
A small bob of mass m = 0.01 kg is hanging from the roof of a moving c...
Understanding the Problem
The problem involves a bob of mass m hanging from the roof of a moving car. The car accelerates horizontally while the bob makes an angle e with the vertical.
Given Data
- Mass of the bob (m) = 0.01 kg
- Acceleration of the car (a) = 2 m/s²
- Angle with the vertical (e) = unknown
Forces Acting on the Bob
1. Weight (W): The force acting downwards due to gravity.
- W = m * g (where g = 9.81 m/s²)
2. Tension (T): The force exerted by the string on the bob, acting along the string.
3. Net Force: Since the car accelerates, the bob experiences an effective horizontal force due to acceleration.
Components of Forces
- The tension can be resolved into two components:
- T*cos(e) = Weight (W)
- T*sin(e) = m * a (horizontal force due to car's acceleration)
Calculating the Tension (T)
1. Calculate Weight (W):
W = 0.01 kg * 9.81 m/s² = 0.0981 N
2. Using the forces:
- T*cos(e) = 0.0981 N
- T*sin(e) = 0.01 kg * 2 m/s² = 0.02 N
3. Finding T:
T = W/cos(e)
T = 0.02 N/sin(e)
4. Combine equations:
Substitute the value of T from the first equation into the second to solve for T and e.
Conclusion
The tension in the string is the solution to the equilibrium of forces acting on the bob, balancing gravitational force and the horizontal force due to the car's acceleration. The exact value of T will depend on the angle e, which can be derived from the above equations.
The problem involves a bob of mass m hanging from the roof of a moving car. The car accelerates horizontally while the bob makes an angle e with the vertical.
Given Data
- Mass of the bob (m) = 0.01 kg
- Acceleration of the car (a) = 2 m/s²
- Angle with the vertical (e) = unknown
Forces Acting on the Bob
1. Weight (W): The force acting downwards due to gravity.
- W = m * g (where g = 9.81 m/s²)
2. Tension (T): The force exerted by the string on the bob, acting along the string.
3. Net Force: Since the car accelerates, the bob experiences an effective horizontal force due to acceleration.
Components of Forces
- The tension can be resolved into two components:
- T*cos(e) = Weight (W)
- T*sin(e) = m * a (horizontal force due to car's acceleration)
Calculating the Tension (T)
1. Calculate Weight (W):
W = 0.01 kg * 9.81 m/s² = 0.0981 N
2. Using the forces:
- T*cos(e) = 0.0981 N
- T*sin(e) = 0.01 kg * 2 m/s² = 0.02 N
3. Finding T:
T = W/cos(e)
T = 0.02 N/sin(e)
4. Combine equations:
Substitute the value of T from the first equation into the second to solve for T and e.
Conclusion
The tension in the string is the solution to the equilibrium of forces acting on the bob, balancing gravitational force and the horizontal force due to the car's acceleration. The exact value of T will depend on the angle e, which can be derived from the above equations.
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A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension?
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A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension?.
A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small bob of mass m = 0.01 kg is hanging from the roof of a moving car in equilibrium making angle e with vertical. If initial velocity of car was zero and acceleration of car is a=2 m/s²calculate wd by tension?.
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