Question

A cart loaded with sand rolls without friction at a velocity v₂ of 1m/sec on a horizontal surface (Fig.). A sphere of mass m equal to 2 kg is projected towards the cart with a horizontal velocity v₁ of 7 m/sec. Upon striking the cart, the sphere embeds itself in the sand. What will be the direction and velocity of the cart after the encounter with the sphere? The mass M of the cart is 10 kg.

Answer 1

Answer: u = 33cm/sec; the cart rolls to the right.

Explanation:

If the vectors directed to the right are taken as positive and those to the left as negative, then the sum of the momenta of the sphere and the cart before they meet is mv₁ — Mv₂ , and after they meet mu + Mu. According to the law of conservation of momentum, mv₁ — Mv₂ = mu + Mu,