The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.110 m and the gun fired vertically as shown, the gun can launch a 23.0-g projectile from rest to a maximum height of 19.0 m above the starting point of the projectile. (a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height. (b) Neglecting all resistive forces, determine the spring constant. (c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure (b).
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.
The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.110 m and the gun fired vertically as shown, the gun can launch a 23.0-g projectile from rest to a maximum height of 19.0 m above the starting point of the projectile.
(a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height.
(b) Neglecting all resistive forces, determine the spring constant.
(c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure (b).
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