This page covers the following topics:
2. Conservation of momentum
3. Elastic and inelastic collisions
4. Force and momentum
All moving objects have momentum. Momentum can be defined as the tendency of an object to keep moving in the same direction and it is a vector quantity. It can be calculated by multiplying mass and velocity, and its unit is kgm/s.
Total momentum is conserved in collisions and explosions unless an external force is exerted on the system. This is called the law of conservation of momentum. The law states that for an isolated system, provided that there are no external forces acting and no energy is provided, momentum will remain constant. For many collision and explosion questions this law results in equating total momentum before and total momentum after.
An explosion is when a rapid change occurs to a stationary system causing objects to move apart. A collision can be elastic or inelastic. Kinetic energy is proportional to the mass of an object and the square of the speed of it. An elastic collision is one in which kinetic energy is conserved, whereas in an inelastic collision, there is no conservation of kinetic energy. Momentum is conserved in both cases as long as a situation meets the conditions for the conservation of momentum.
By Newton's second law, a force is given by F = m × a. Substituting the acceleration equation into this gives F × t = mv − mu. Given that v is the final velocity and u is the initial velocity, mv − mu = change in momentum. This is a way to derive an equation relating the rate of change of momentum and force.
Change in momentum is also known as impulse and force is also known as the rate of change of momentum. Newton's second law can be rewritten as: a force acting on a body is proportional to the rate of change of momentum it produces in its direction.
Impulse is defined as the change of momentum of an object and is given in Ns. It can be calculated using impulse = force × time or by finding the area under a force-time graph. Units Ns and kgm/s can be used interchangeably as they have the same physical meaning.
Two particles are moving towards each other when they collide. The collision causes both particles to stop. Explain whether the collision is elastic or inelastic.
An elastic collision is defined as one in which no kinetic energy is lost. Before the collision, the two particles are moving, meaning that there is kinetic energy. After the collision, both particles are at rest, so there is no kinetic energy. Kinetic energy is not conserved in the collision, therefore it is an inelastic one.
Inelastic since kinetic energy is not conserved.
When a car crashes, an airbag inflates in front of the driver. Explain, using ideas about rate of change of momentum, how an airbag reduces the possibility of injury during a car crash.
Since F × t = change in momentum, the airbag increases the time taken to reduce momentum to 0, as it ensures that it takes more time for the driver to stop. A greater time period reduces the force that acts on the driver, therefore reducing the risk of injury.
F × t = change in momentum; airbag increases time, therefore reducing force.
A car is travelling in a straight line at a constant velocity of 11 m/s. Given that the momentum of the car is 15125 kgm/s, find the mass of the car.
p = m × v
15125 kgm/s = mass × 11 m/s
mass = 15125 ÷ 11 = 1375 kg
Find the impulse exerted on an object, given the force-time diagram.
impulse = area under force-time graph
impulse = 0.5 × 70 N × 4 s + 0.5 × (70 N + 85 N) × 4 s + 0.5 × 85 N × 7 s = 747.5 Ns
Two go-karts of equal mass are travelling towards each other and collide. The first go-kart is travelling towards the right at 4 m/s and the second is travelling towards the left at 2.75 m/s. Given that the first go-kart changes direction after the collision and has a speed of 2 m/s, find the velocity of the second go-kart after the collision.
By the law of conservation of momentum, total momentum before = total momentum after.
mass × 4 m/s − mass × 2.75 m/s = mass × velocity − mass × 2 m/s
Since the masses of the two go-karts are equal, we can cancel mass out of the equation.
velocity = 4 − 2.75 + 2 = 3.25 m/s to the right
3.25 m/s to the right
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