Question

1.3 The equation mv gl sin 0 +kl2 describes the energy of an object with mass m amd initial speed vo sliding a distance l up a frictionless ramp at inclination angle θ, all the while compressing a spring with stiffness k as it comes to rest. Solve the equation for I, the distance the object moves up the incline and compresses the spring.

Answer 1

1/2 mv_0^2 mg l sin theta + 1/2 k l^2 l^2 + (29 sin theta/k) l - m/k v_0^2 = 0 l = -2g sin theta/16 plusminus squareroot (2g sin that/k)^2 + 4 times mv^2/k/2 l = -g sin theta/k + squareroot g^2 sin theta/k^2 + mv^2_0/k (or) -g sin teta/k - squareroot g^2 sin theta/k62 + mv_0^2/k