A spring with spring constant k = 80 N/m has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.5 m and a mass of m = 1.8 kg is placed at its free end on a frictionless slope which makes an angle of θ = 37° with respect to the horizontal. The spring is then released. [Note: you may use the approximations sin 37° = 0.6 and cos 37° = 0.8 for simplicity] a) If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest? b) If the mass is attached to the spring, how far up the slope will the mass move before coming to rest? c) Now the incline has a coefficient of kinetic friction μk. If the block, attached to the spring, is observed to stop just as it reaches the spring’s equilibrium position, what is the coefficient of friction?
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 spring with spring constant k = 80 N/m has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.5 m and a mass of m = 1.8 kg is placed at its free end on a frictionless slope which makes an angle of θ = 37° with respect to the horizontal. The spring is then released. [Note: you may use the approximations sin 37° = 0.6 and cos 37° = 0.8 for simplicity]
a) If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest?
b) If the mass is attached to the spring, how far up the slope will the mass move before coming to rest?
c) Now the incline has a coefficient of kinetic friction μk. If the block, attached to the spring, is observed to stop just as it reaches the spring’s equilibrium position, what is the coefficient of friction?
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