First slide

Concept of potential energy

Question

A 15 g ball is shot from a spring gun whose spring has a force constant of 600 N/m. The spring is compressed by 5 cm. The greatest possible horizontal range of the ball for this compression is (g = 10 m/s²)

Moderate

A

6.0 m
B

10.0 m
C

12.0 m
D

8.0 m

Solution

For getting horizontal range, there must be some inclination of spring with ground to project ball.
$\Rightarrow R_{\max} = \frac{u^{2}}{g}$ …..(i)
But K.E. acquired by ball = P.E. of spring gun
$\Rightarrow \frac{1}{2} {mu}^{2} = \frac{1}{2} {kx}^{2} \Rightarrow u^{2} = \frac{{kx}^{2}}{m}$ …..(ii)
From equation (i) and (ii)
$R_{\max} = \frac{{kx}^{2}}{mg} = \frac{600 \times {(5 \times 10^{- 2})}^{2}}{15 \times 10^{- 3} \times 10}$ =10m.

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