Question

A dart of mass 0.5 kg is pressed against the spring of a dart gun the spring k=300n/m is compressed 10 cm and released. If the dart detaches from the spring when the latter reaches its normal length what speed does the dart acquire?

Answer 1

v = 2.45 m/s

Step-by-step explanation:

given,

mass of the dart = 0.5 Kg

spring constant of the dart = k = 300 N/m

compressed distance = 10 cm = 0.1 m

speed acquire by the cart = ?

we know,

using conservation of energy

kinetic energy will be equal to spring energy

`(1)/(2)mv^2 = (1)/(2)kx^2`

`mv^2 = kx^2`

`v^2 = (kx^2)/(m)`

`v = x\sqrt{(k)/(m)}`

`v = 0.1\sqrt{(300)/(0.5)}`

`v = 0.1* 24.495`

v = 2.45 m/s

speed acquire by the dart is equal to v = 2.45 m/s