Elastic and inelastic collisions in one and two dimensions
- Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v_1 while body B is at rest before collision. The velocity of the system after collision is v_2. The ratio v_1 : v_2 is : Answer: 3. 2:1 Key idea: In a completely inelastic collision the bodies stick together and momentum is conserved. mv₁+0=(m+m)v₂ , so v₂=v₁/2... 1
- Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is : Answer: 2. 8/9 Use the formula for the final speed of a body in a head-on elastic collision with a body at rest. v_A=m₁-m₂/m₁+m₂u=4m-2m/4m+2... 1
- A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be Answer: 3. 0.25 Momentum conservation: mv=0+4mv₂⇒ v₂=v/4 (lighter block at rest, v₁=0 ). Coefficient of restitution = relative speed of sepa... 1
- A bullet of mass 10 g moving horizontally with a velocity of 400 m s^-1 strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical d… Answer: 2. 120 m s ⁻¹ Use energy for the swing of the block and momentum conservation for the collision. Block after impact: v=√(2gh)=√(2×10... 1
- Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be Answer: 1. 0.5 m/s and -0.3 m/s For an elastic head-on collision between two identical masses, the bodies simply exchange velocities. (Momen... 1