|
109. Problem 16.44E (HRW) A (hypothetical) large slingshot is stretched 1.50 m to launch a 130 g projectile with speed sufficient to escape from Earth (11.2 km/s). We can assume that the elastic sling shot obeys Hook’s law. We have to find (a) the spring constant of the device, if all the elastic energy is converted to kinetic energy. (b) Assuming that an average person can exert a force of 220 N, we have to estimate the number of people required for stretching the slingshot. |
|
Solution: Click For PDF Version (a) The spring constant, k, of the device can be determined by requiring
that the potential energy of the slingshot will be
where
Elastic force exerted on the slingshot in this situation is
(b) It is given that an average person can exert a force of 220 N. Therefore, the number of persons needed to stretch the slingshot as per the data of the problem would be
|
,
as the slingshot obeys Hook’s law and a is the maximum stretch. As the
potential energy of the slingshot is fully converted into kinetic energy of the
projectile, we have the condition
is the
speed with which the projectile of mass
is
released from the stretched slingshot. As the projectile is released with the
escape velocity of the Earth,
. We
calculate the value of the spring constant
