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A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..?
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A mass of 0.1 kg is rotated in vertical circle using a string of lengt...
Understanding the Problem
To find the tangential acceleration of the mass when it is at an angle of 60° with the vertical, we first need to identify the forces acting on the mass and the components of acceleration involved in circular motion.
Given Data
- Mass (m) = 0.1 kg
- Length of string (r) = 20 cm = 0.2 m
- Angle (θ) = 60°
- Speed (v) = 0.5 m/s
Analysis of Forces
- The gravitational force acting on the mass is given by:
Weight (W) = m * g = 0.1 kg * 9.81 m/s² = 0.981 N
- At the angle of 60°, the components of the weight can be resolved as:
- Vertical component (W_vertical) = W * cos(θ)
W_vertical = 0.981 * cos(60°) = 0.981 * 0.5 = 0.4905 N
- Horizontal component (W_horizontal) = W * sin(θ)
W_horizontal = 0.981 * sin(60°) = 0.981 * (√3/2) ≈ 0.8507 N
Tangential Acceleration Calculation
- The tangential acceleration (a_t) is related to the net force acting along the tangent to the circular path. Here, the tangential force is primarily due to the weight's horizontal component.
- Using Newton's second law:
a_t = F_t / m
where F_t is the tangential force, which can be approximated as W_horizontal in this scenario.
- Thus, substituting the values:
a_t = W_horizontal / m = 0.8507 N / 0.1 kg = 8.507 m/s²
Conclusion
The tangential acceleration of the mass at that instant when the string makes an angle of 60° with the vertical is approximately 8.51 m/s².
To find the tangential acceleration of the mass when it is at an angle of 60° with the vertical, we first need to identify the forces acting on the mass and the components of acceleration involved in circular motion.
Given Data
- Mass (m) = 0.1 kg
- Length of string (r) = 20 cm = 0.2 m
- Angle (θ) = 60°
- Speed (v) = 0.5 m/s
Analysis of Forces
- The gravitational force acting on the mass is given by:
Weight (W) = m * g = 0.1 kg * 9.81 m/s² = 0.981 N
- At the angle of 60°, the components of the weight can be resolved as:
- Vertical component (W_vertical) = W * cos(θ)
W_vertical = 0.981 * cos(60°) = 0.981 * 0.5 = 0.4905 N
- Horizontal component (W_horizontal) = W * sin(θ)
W_horizontal = 0.981 * sin(60°) = 0.981 * (√3/2) ≈ 0.8507 N
Tangential Acceleration Calculation
- The tangential acceleration (a_t) is related to the net force acting along the tangent to the circular path. Here, the tangential force is primarily due to the weight's horizontal component.
- Using Newton's second law:
a_t = F_t / m
where F_t is the tangential force, which can be approximated as W_horizontal in this scenario.
- Thus, substituting the values:
a_t = W_horizontal / m = 0.8507 N / 0.1 kg = 8.507 m/s²
Conclusion
The tangential acceleration of the mass at that instant when the string makes an angle of 60° with the vertical is approximately 8.51 m/s².
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A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..?
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A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..?.
A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of 0.1 kg is rotated in vertical circle using a string of length 20 cm when the string makes an angle 60° with vertical the speed of the mass is q.5 m/s the tangential acceleration of the mass at that instant is..?.
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