catapult has a spring constant of 20 N/m and is pulled back 5 cm. Calculate the initial speed of the projectile if it has a mass of 0.1 kg.

Answer 1

The force to compress the spring is 20N/m of compression.

Therefore, the force to compress it 5cm is 5/100 x 20N = 1.0N

The projectile has a mass of 0.1kg, so using Newton’s Second law (for constant mass),

F = ma

1.0N = 0.1a

a = 1.0/0.1 = 10 m/s²

The spring's stored potential energy is represented as Ep = ½kx² where k is the spring constant and x is the compression distance.

Ep = ½(20)(0.05^2) = 0.025J

This energy is converted to kinetic energy when the spring is released, so Ek = 0.025J

Now we will find the velocity using the equation

Ek = ½mv^2 for the projectile,

Solving for v, we get

0.025 = ½(0.1)v²

or 0.5 = v²

Then v =√0.5 = 0.7071m/s

So the initial velocity of the projectile is 0.7071m/s