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A 1.01 kg mass is attached to a spring of force constant 10.1 N/cm and placed on a frictionless surface. By how much will the spring stretch
Question
A 1.01 kg mass is attached to a spring of force constant 10.1 N/cm and placed on a frictionless surface. By how much will the spring stretch if the mass moves along a circular path of radius 0.515 m at a rate of 1.84 revolutions per second
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Physics
3 years
2021-07-27T11:43:02+00:00
2021-07-27T11:43:02+00:00 1 Answers
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Answers ( )
Answer:
6.88 cm
Explanation:
Given that:
mass m of the object = 1.0 kg
Force constant of the spring (k) = 10.1 N/cm = 10.1 × (100) N/m
= 1010 N/m
Radius of the circular path R = 0.515 m
Since 1 revolution = 2 π radian
angular speed of the object ω = 1.84 rev/s = 1.84 × ( 2 π) rad/s
= 11.56 rad/s
Amount of the spring that stretches = X???
However, the amount of the force the spring exerts on the object due to the stretching is directly equal to the centripetal force required by the object for the circular motion:
SO;
X = 0.0688 m
Hence, the amount of the spring stretches = 6.88 cm