Question

Lola's kids are riding around in their slelds. Greg hops in his sled and goes down a snow bank. He slides down the hill and continues moving on a horizontal surface at the bottom of the hill. That's where he finds Marg, who is in her sled at rest, but attached to a spring that is also attached to a wall. The spring compresses after the Greg/sled combo hits the Marg/sled combo at 15m/s. The Greg/sled combo and Marg/sled combo start to be moving together at the same speed after they collide and becom epermanently stuck together. The mass of the Greg/sled combo is 200g, the mass of the Marg/sled combo is 250g, and a spring constant is 1300N/m. Assume whole system is frictionless.

(a) What is the velocity of Greg/sled and Marg/sled combo after they collide; work algebra first, then plug in numbers (a-d).

(b) What is the maximum compression of the spring after collision?

(c) There is no friction losses and mechanical energy is conserved, the children form an oscillator tht is not damped over time. What is the period of the child oscillator.

(d) What is the maximum acceleration of Greg/s'ed and Marg/s;ed combo and where does this occur?

Answer 1

a) Apply conservation of momentum

200*15 = (200 + 250)*v

==> v = 200*15/(200 + 250)

= 6.67 m/s

b) Apply conservation of energy

(1/2)*k*x^2 = (1/2)*(m1 + m2)*v^2

x^2 = (1/2)*(m1 + m2)*v^2/k

x = sqrt( (m1+m2)*v^2/(2*k))

= sqrt( (0.2 + 0.25)*6.67^2/(2*1300))

= 0.088 m or 8.8 cm

c)
Time period, T = 2*pi*sqrt( (m1+m2)/k)

= 2*pi*sqrt((0.2 + 0.25)/1300)

= 0.117 s

d) maximum acceeration, a_max = k*x_max/(m1+m2)

= 1300*0.088/(0.2 + 0.25)

= 254 m/s^2

It occurs when spring compression becomes maximum.