A tractor of mass 5.0 × 10³kg is used to tow a car of mass 2.5 × 10³kg. The tractor moved with a speed of 3.0m/s just before the towing rope became taul, calculate the;speed of the tractor immediately the rope becomes taul, loss kinetic energy of the system just after the car has started moving,,impulse in the rope when jerbs it in the car into motion

Speed of the tractor after the rope becomes taul = 2 m/s

Loss of kinetic energy =

33.33% or 7,500 J

Total kinetic energy before the collision/impact = 22,500 J

Total kinetic energy after the collision/impact = 15,000 J

Explanation:

To solve this problem, you can use the formulas involving the conservation of momentum because there is a type of collision involved as momentum is the product of mass and velocity (speed with direction). This is all revolved around newton's second law.

p (momentum) = mv (mass × velocity)

Because no external forces act on this system, the total momentum before the collision is the same as the total momentum after.

This can be represented by:

m1u1 + m2u2 = m1v1 + m1v2 [This is the general formula because most of the others are just variations]

u = initial velocity.

m = mass.

v = final velocity.

To determine the type of collision involved, you must compare the initial and final kinetic energy of the system as well as it's initial and final velocities.

If the kinetic energy is different and the objects stick together or have the sam final velocity, the type of collision is perfectly inelastic. [The conservation of momentum applies like all collisions, but the maximum amount of kinetic energy is lost] [example: this problem]

If the kinetic energy is different but the objects do not stick together or don't have the same final velocity, the type of collision is partially elastic/inelastic. [example: car crash] [conservation of momentum applies, while the conservation of kinetic energy doesn't]

If the kinetic energy is the same, the collision type is simply perfectly elastic. [Both the conservation of kinetic energy, and momentum applies] [example: newton's cradle; the one with the swinging metallic balls]

Interestingly enough, an explosion is basically the reverse of an inelastic collision.

Perfectly inelastic:

m1u1 + m2u2 = v(m1 + m2)

Partially elastic:

m1u1 + m2u2 = m1v1 + m2v2

In this case if an object is carried or pulled without an additional force as in towed, this type of collision must be perfectly inelastic.