A children's toy comprises a plastic semi-sphere mounted on top of a spring of spring constant 5×103 Nm−1 . The total mass of the toy is 25 g. The toy is used by compressing the spring by 1 cm. When it is let go, the toy jumps into the air. ( g=10 ms−2 )
(a) Calculate the force in the fully compressed spring.
(b) Calculate the initial acceleration of the toy as the spring starts its return to its uncompressed length.
(c) Once the spring has regained its uncompressed length, the toy experiences only its downwards acceleration due to gravity. The time for this to happen is 4.5 ms. If we consider that the initial acceleration upwards decreases linearly with the compressed length of the spring, show that the initial speed at which the toy moves upwards is 4.48 ms−1 .
(d) Calculate how high the toy can jump into the air.