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A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone?
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A stone tied to the end of string 80cm long is whirled in a horizontal...
Given data:
- Length of string (r) = 80 cm = 0.8 m
- Number of revolutions (n) = 14
- Time taken (t) = 25 s
Calculating the radius:
- The length of the string is equal to the circumference of the circle.
- So, 2πr = L
- 2πr = 0.8 m
- r = 0.8 / (2π) m
- r ≈ 0.127 m
Calculating the time period:
- The time period (T) is the time taken for one complete revolution.
- T = t / n
- T = 25 s / 14
- T ≈ 1.786 s
Calculating the angular velocity:
- The angular velocity (ω) is the rate of change of angle with respect to time.
- ω = 2π / T
- ω = 2π / 1.786 s
- ω ≈ 3.527 rad/s
Calculating the linear velocity:
- The linear velocity (v) is the rate of change of displacement with respect to time.
- v = ωr
- v = 3.527 rad/s * 0.127 m
- v ≈ 0.448 m/s
Calculating the acceleration:
- The acceleration (a) is the rate of change of velocity with respect to time.
- a = v^2 / r
- a = (0.448 m/s)^2 / 0.127 m
- a ≈ 1.581 m/s^2
Result:
The magnitude of acceleration of the stone is approximately 1.581 m/s^2.
- Length of string (r) = 80 cm = 0.8 m
- Number of revolutions (n) = 14
- Time taken (t) = 25 s
Calculating the radius:
- The length of the string is equal to the circumference of the circle.
- So, 2πr = L
- 2πr = 0.8 m
- r = 0.8 / (2π) m
- r ≈ 0.127 m
Calculating the time period:
- The time period (T) is the time taken for one complete revolution.
- T = t / n
- T = 25 s / 14
- T ≈ 1.786 s
Calculating the angular velocity:
- The angular velocity (ω) is the rate of change of angle with respect to time.
- ω = 2π / T
- ω = 2π / 1.786 s
- ω ≈ 3.527 rad/s
Calculating the linear velocity:
- The linear velocity (v) is the rate of change of displacement with respect to time.
- v = ωr
- v = 3.527 rad/s * 0.127 m
- v ≈ 0.448 m/s
Calculating the acceleration:
- The acceleration (a) is the rate of change of velocity with respect to time.
- a = v^2 / r
- a = (0.448 m/s)^2 / 0.127 m
- a ≈ 1.581 m/s^2
Result:
The magnitude of acceleration of the stone is approximately 1.581 m/s^2.
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A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone?
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A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone?.
A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone tied to the end of string 80cm long is whirled in a horizontal circle with a constant speed . If the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone?.
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