5. A hoop of radius 0.20 m and a mass of 0.35 kg is released from rest and allowed to roll down an inclined plane. What is the translational speed (v) of the hoop after dropping a vertical distance of 3.80 m? m/s
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![### Physics Problem: Rolling Motion of a Hoop
#### Problem Statement:
A hoop of radius 0.20 m and a mass of 0.35 kg is released from rest and allowed to roll down an inclined plane. What is the translational speed (v) of the hoop after dropping a vertical distance of 3.80 m?
#### Answer:
[ ] m/s
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#### Explanation:
This physics problem involves understanding the concepts related to the conservation of energy as it pertains to rotational motion. The problem requires the application of both kinetic energy (translational and rotational) and potential energy considerations to find the translational speed of the hoop.
Students are encouraged to analyze the energy transformations that occur as the hoop rolls down the incline and derive the final speed using the relationship between gravitational potential energy and kinetic energy.
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This text and the problem can be used as part of an educational module on rotational dynamics in a high school or undergraduate physics course.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c06aee-69db-4b48-aaad-c9b35ad590a4%2F8fe6a7f8-2740-4232-a7bb-528d05d1ea55%2F28a4q7r_processed.png&w=3840&q=75)
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