Question

A 3.0 kg object is loaded into a toy spring gun, and the spring has a spring constant 750N/m. The object compresses the spring by 8.0 cm. The gun is tilted at an angle 30.0 degrees above the horizontal.

a. Once the ball is launched, is the minimum kinetic energy greater than or equal to zero? Explain your reasoning.
b. How high does the object go (relative to its height as it leaves the gun)?

Answer 1

Step-by-step explanation:

mass of object, m = 3 kg

spring constant, K = 750 n/m

compression, x = 8 cm = 0.08 m

angle of gun, θ = 30°

(a) As the ball is launched, it has some velocity due to the compression in the spring, so it has some kinetic energy.

(b) Let v be th evelocity of ball at the tim eof launch.

by using the conservation of energy

1/2 Kx² = 1/2 mv²

750 x 0.08 x 0.08 = 3 x v²

v = 1.265 m/s

By use of the formula of maximum height

`h = (v^(2)Sin^(2)\theta)/(2g)`

`h = (1.265^(2)Sin^(2)30)/(2* 9.8)`

h = 0.02 m

h = 2 cm