A small block of mass M = 150 g is placed on top of a larger block of mass 3M which is placed on a level frictionless surface and is attached to a horizontal spring of spring constant k = 9.6 N/m. The coefficient of static friction between the blocks is μ = 0.2. The lower block is pulled until the attached spring is stretched a distance D = 2.5 cm and released. A: Assuming the blocks are stuck together, what is the maximum magnitude of acceleration amax of the blocks in terms of the variables in the problem statement? B: Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m/s2. C: Write an equation for the largest spring constant kmax for which the upper block does not slip. D: Calculate a value for the largest spring constant kmax for which the upper block does not slip, in N/m.
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 small block of mass M = 150 g is placed on top of a larger block of mass 3M which is placed on a level frictionless surface and is attached to a horizontal spring of spring constant k = 9.6 N/m. The coefficient of static friction between the blocks is μ = 0.2. The lower block is pulled until the attached spring is stretched a distance D = 2.5 cm and released.
A: Assuming the blocks are stuck together, what is the maximum magnitude of acceleration amax of the blocks in terms of the variables in the problem statement?
B: Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m/s2.
C: Write an equation for the largest spring constant kmax for which the upper block does not slip.
D: Calculate a value for the largest spring constant kmax for which the upper block does not slip, in N/m.
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