A 1.0-kg block (m1) is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with an angle θ = 60° to the vertical as shown in the figure. At the lowest point in its swing when it is moving horizontally, the block collides elastically with another block of mass m2 = 2.0-kg initially at rest on a horizontal surface which is frictionless except for a length of 1.5 m, where the coefficient of kinetic friction is 0.25 (see the figure below). After the collision the second block move towards the spring of force constant k = 10000 N/m which is fixed at one end of the surface (see the figure below). Answer the following questions. (a) Calculate the velocity of m1 just before the collision. (b) Calculate the velocities of m1 and m2 just after the collision. (c) Calculate the maximum height to which m1 rises after the collision.
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 1.0-kg block (m1) is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with an angle θ = 60° to the vertical as shown in the figure. At the lowest point in its swing when it is moving horizontally, the block collides elastically with another block of mass m2 = 2.0-kg initially at rest on a horizontal surface which is frictionless except for a length of 1.5 m, where the coefficient of kinetic friction is 0.25 (see the figure below). After the collision the second block move towards the spring of force constant k = 10000 N/m which is fixed at one end of the surface (see the figure below). Answer the following questions.
(a) Calculate the velocity of m1 just before the collision.
(b) Calculate the velocities of m1 and m2 just after the collision.
(c) Calculate the maximum height to which m1 rises after the collision.
(d) Calculate the maximum compression, xc, of the spring.
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