A package of mass mmm = 6.00 kgkg is released on a 53.1∘∘ incline, a distance DDD = 4.00 mm from a long spring with force constant 1.10×102N/m1.10×102N/m that is attached at the bottom of the incline (Figure 1). The coefficients of friction between the package and incline are μsμs = 0.400 and μkμkmu_k = 0.200. The mass of the spring is negligible. (a) What is the maximum compression of the spring? (b) The package rebounds up the incline. When it stops again, how close does it get to its original position? (c) What is the change in the internal energy of the package and incline from the point at which the package is released until it rebounds to its maximum height?
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.
A package of mass mmm = 6.00 kgkg is released on a 53.1∘∘ incline, a distance DDD = 4.00 mm from a long spring with force constant 1.10×102N/m1.10×102N/m that is attached at the bottom of the incline (Figure 1). The coefficients of friction between the package and incline are μsμs = 0.400 and μkμkmu_k = 0.200. The mass of the spring is negligible. (a) What is the maximum compression of the spring? (b) The package rebounds up the incline. When it stops again, how close does it get to its original position? (c) What is the change in the internal energy of the package and incline from the point at which the package is released until it rebounds to its maximum height?
a)
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