Energy Transfer In Elastic Collisions

Question

A 1 kg ball moving along a frictionless track strikes a stationary 3 kg ball in a perfectly elastic head-on collision. What fraction of the incoming ball's kinetic energy is transferred to the heavier ball?

RankGuru · Accepted Answer

For a one-dimensional elastic collision in which a mass $m_1$ strikes a stationary mass $m_2$, the fraction of kinetic energy transferred to the target is $\dfrac{4 m_1 m_2}{(m_1 + m_2)^2}$, a result derived by combining momentum and kinetic-energy conservation. Substituting $m_1 = 1	ext{ kg}$ and $m_2 = 3	ext{ kg}$ gives $\dfrac{4 	imes 1 	imes 3}{(1+3)^2} = \dfrac{12}{16} = 0.75$, or 75%. The option 25% reports the fraction the lighter ball retains rather than transfers. The option 50% would only hold for equal masses, which is not the case here. The option 100% wrongly assumes the incoming ball stops, true only for equal masses. The transfer fraction reaches its maximum value of unity only when the two masses are exactly equal, and it falls off whether the target is made much heavier or much lighter than the projectile. This very principle explains why neutrons are slowed most efficiently by collisions with light nuclei of comparable mass, such as hydrogen, in the moderators of nuclear reactors. This applies the NCERT energy-transfer formula for unequal-mass elastic collisions. As a check, the retained fraction must be $\left(\dfrac{m_1-m_2}{m_1+m_2}ight)^2 = \left(\dfrac{-2}{4}ight)^2 = 0.25$, and $0.75 + 0.25 = 1$ confirms total energy conservation.

Energy Transfer In Elastic Collisions

Select the correct option:

🔒 Solution Hidden from View

More work, energy and power Practice Questions

A rubber ball is dropped from a height of 2 m onto a hard floor and rebounds to a height of 1.28 m a...

A satellite moves in a perfectly circular orbit around the Earth under the gravitational pull direct...

A cyclist of total mass 70 kg rides up a slope inclined at 30 degrees to the horizontal at a steady ...

A small stone tied to a string is whirled in a vertical circle of radius 2 m. What is the minimum sp...

Two bodies of different masses possess the same magnitude of linear momentum while moving in a strai...

A ball is thrown vertically upward and returns to the same height from which it was launched on a wi...

A stone of mass 0.5 kg is dropped from rest at a height of 8 m above the ground. Ignoring air resist...

A weightlifter raises a barbell of mass 80 kg from the floor to a height of 2 m above the floor in 4...

A 2 kg lump of clay moving at 6 m/s strikes and sticks to a 4 kg block initially at rest on a fricti...

A car engine delivers a constant power of 50 kW while the car moves at a steady speed of 25 m/s alon...

A wooden crate of mass 10 kg is dragged 5 m up a rough incline by a force, and friction exerts a con...

Which of the following statements correctly distinguishes a conservative force from a non-conservati...

About This Question

Solution