Question

a toy gun consist of a spring and rubber dart mass 16g when compress by 4cm and release it project the dart to a height of 2m if compressed by 6cm height achieve


any one can give this answer I will mark you as a brainllist ​

Answer 1

Answer:

4.5 m

Explanation:

Mass of rubber dart = 16 gm = 0.016 kg.

x ₁ = Compression of spring = 4 cm = 0.04 m.

Height reached by dart = 2 m.

If we neglect any loss of energy during this process, then elastic potential energy will be appear as gravitational potential energy at max height.

Keeping this in mind,

Elastic PE of spring = Uₐ = 1/2kx₁² (where k is the spring constant)

ΔUₓ = Change in Potential energy - mgh₁

=> Uₐ = ΔUₓ => 1/2kx₁² = mgh₁ ----- [1]

Now When x₂ = compression of spring = 6 cm = 0.06 m,

Let the height it goes to be h₂.

=> Uₐ = ΔUₓ => 1/2kx₂² = mgh₂ ---------------- [2].

From [1] and [2],

(x₁/x₂)² = h₁/h₂

=> h₂ = h₁ * (x₂/x₁)² = 2 * (0.06/0.04)² = 9/4 * 2 = 9/2 = 4.5 m.

So the height achieved = 4.5 m.