Momentum

Define conservation of momentum

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it.

Momentum is a product of an object's mass and velocity, expressed as p = mv.

In a collision, the sum of the momenta before the collision is equal to the sum of the momenta after the collision.

This conservation applies to both elastic and inelastic collisions, though kinetic energy is not necessarily conserved in inelastic collisions.

External forces can include friction, air resistance, or any force that is not included within the closed system.

Mathematically, for a system of particles, the law is expressed as ∑ p{before} = ∑ p{after}.

Calculate impulse momentum

Formula for change in momentum: Δp = pf - pi

Formula for momentum: p = mv

Formula relating force and change in momentum: $Δp = FΔt$

p: momentum (kg m/s)

m: mass (kg)

v: velocity (m/s)

F: average force (N)

Δt: time interval (s)

Calculate velocity

Question: An object of mass 2kg moving at 3ms^-1 collides with a stationary object of mass $4kg. Calculate the velocity of the combined object after the collision.

Step 1: Identify the masses and velocities of the objects before the collision. (e.g., $m_1 = 2kg, v_1 = 3ms^-1, m_2 = 4kg, v_2 = 0ms^-1.

Step 2: Write the formula for the law of conservation of momentum: $m_1v_1 + m_2v_2 = (m_1 + m_2)v_f.

Step 3: Substitute the known values into the equation. (e.g., 2kg times 3ms^-1 + (4 kg times 0ms^-1 = (2kg + 4kg v_f).

Step 4: Solve the equation for the final velocity v_f. (e.g., 6 = 6v_f, so v_f = 1ms^-1).

Calculate mass

Question: An object with a mass of 5 kg moving at a velocity of 10 m/s collides with a stationary object and they stick together. The velocity of the combined object after the collision is 4 m/s. Using the conservation of momentum, calculate the mass of the stationary object.

Step 1: List the given values: m_1 (mass of the first object), v_1 (initial velocity of the first object), m_2 (mass of the second object), v_2 (initial velocity of the second object), and v_f (final velocity).

Step 2: Write the momentum conservation equation: m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f.

Step 3: Plug in the known values into the momentum conservation equation.

Step 4: Rearrange the formula to solve for the unknown mass, m_2.

Step 5: Calculate the unknown mass, m_2, using the rearranged equation.

Use the formula p = mv

Formula for momentum: p = mv

Momentum p: The quantity of motion of a moving body, measured as a product of its mass and velocity; units are kg.m/s

Mass m: The amount of matter in an object; measured in kilograms (kg)

Velocity v: The speed of an object in a specific direction; measured in metres per second ms^-1