The Momentum Calculator helps you solve momentum problems step by step. Calculate linear momentum (p = mv), impulse (J = F times t), and analyse two-body collisions including both elastic and inelastic types.
Enter your values and get instant results with detailed working. The calculator covers four modes: linear momentum, impulse and change in momentum, conservation of momentum for two-body collisions, and elastic versus inelastic collision analysis.
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Momentum is the product of an object's mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of momentum is kg m/s.
The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum: J = delta p = F times delta t. This connects force acting over time to changes in motion.
The law of conservation of momentum states that in an isolated system (no external forces), the total momentum before and after a collision remains the same. This principle applies to all types of collisions.
In an elastic collision, both momentum and kinetic energy are conserved. In a perfectly inelastic collision, momentum is conserved but the objects stick together and kinetic energy is lost (converted to heat, sound, or deformation).
Problem: A 5 kg ball moves at 3 m/s. What is its momentum?
Solution: p = mv = 5 times 3 = 15.
Answer: 15 kg m/s
Problem: A force of 200 N acts on a ball for 0.05 s. What is the impulse?
Solution: J = F times delta t = 200 times 0.05 = 10.
Answer: 10 N s
Problem: A 4 kg cart at 6 m/s hits a stationary 2 kg cart. They stick together. Find the final velocity.
Solution: m1*v1 + m2*v2 = (m1+m2)*vf. So 4*6 + 2*0 = 6*vf. vf = 24/6 = 4.
Answer: 4 m/s
Problem: A 2 kg ball at 5 m/s hits a 3 kg ball at rest. Find the final velocities (elastic).
Solution: v1f = ((2-3)/(2+3))*5 = -1. v2f = (2*2/(2+3))*5 = 4.
Answer: v1f = -1 m/s, v2f = 4 m/s
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