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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.
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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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