Question

In a physics lab experiment, a compressed spring launches a 29 g metal ball at a 35 ∘ angle. Compressing the spring 18 cm causes the ball to hit the floor 1.8 m below the point at which it leaves the spring after traveling 5.4 m horizontally.

What is the spring constant?

Answer 1

here,

mass , m = 0.029 kg

theta = 35 degree

x = 0.18 m

ho = 1.8 m

range , R = 5.4 m

let the spring constant be k

time taken be t and initial speed be u

- h0 = u*sin(theta) * t + 0.5 * a * t^2

- 1.8 = u*sin(35) * t - 0.5 * 9.8 * t^2 .....(1)

and

u * cos(theta) * t = R

u * cos(35) * t = 5.4 ....(2)

and for the spring

0.5 * k * x^2 = 0.5 * m * u^2

k * 0.18^2 = 0.029 * u^2 ...(1)

using(1) , (2) and (3)

k = 34.14 N/m

the spring constant is 34.14 N/m