a tractor of mass 5.0×10^3kg is used to tow a car of mass 2.5×10^3kg. The tractor moved with a speed of 3.0m/s just before the towing rope became taut.

1. Find the speed of the tractor immediately the rope becomes taut
2. loss in kinetic energy of the system just after the car has started moving
3. impulse in the rope when it jerks the car into motion

Given:

M1 = 5000kg, Vi = 3m/s.
M2 = 2500kg, V2 = 0 before taut.
V3 = Velocity of M1 after taut(tight).

Momentum before taut = Momentum after taut.
M1*V1 = (M1+M2)V3.
5000 * 3 = 7500*V3,
V3 = 2 m/s.

Note: The car is not a part of the system until the rope becomes taut(tight).

The like are not complete and the solution is in short ways

Define the word; IMPULSE

I need an answer

1. When the rope becomes taut, the tractor and the car start moving as one system. To find the speed of the tractor immediately after the rope becomes taut, we need to use the principle of conservation of momentum.

The initial momentum of the system (before the rope becomes taut) is given by:
initial momentum = (mass of tractor) × (initial speed of tractor) + (mass of car) × 0
initial momentum = (5.0×10^3 kg) × (3.0 m/s) + (2.5×10^3 kg) × 0
initial momentum = 15,000 kg·m/s

Since momentum is conserved, the final momentum of the system (after the rope becomes taut) will also be 15,000 kg·m/s. Let's assume the final speed of the tractor is v m/s.

final momentum = (mass of tractor) × (final speed of tractor) + (mass of car) × (final speed of car)
15,000 kg·m/s = (5.0×10^3 kg) × v + (2.5×10^3 kg) × v

Combining like terms and solving for v, we get:
v = 15,000 kg·m/s / (5.0×10^3 kg + 2.5×10^3 kg)
v = 15,000 kg·m/s / 7.5×10^3 kg
v = 2.0 m/s

Therefore, the speed of the tractor immediately after the rope becomes taut is 2.0 m/s.

2. The loss in kinetic energy of the system just after the car has started moving can be calculated by finding the initial kinetic energy and subtracting the final kinetic energy.

Initial kinetic energy = (1/2) × (mass of tractor) × (initial speed of tractor)^2 + (1/2) × (mass of car) × 0^2
Initial kinetic energy = (1/2) × (5.0×10^3 kg) × (3.0 m/s)^2 + (1/2) × (2.5×10^3 kg) × 0
Initial kinetic energy = 22,500 J

Final kinetic energy = (1/2) × (mass of tractor) × (final speed of tractor)^2 + (1/2) × (mass of car) × (final speed of car)^2
Final kinetic energy = (1/2) × (5.0×10^3 kg) × (2.0 m/s)^2 + (1/2) × (2.5×10^3 kg) × (2.0 m/s)^2
Final kinetic energy = 10,000 J

Loss in kinetic energy = Initial kinetic energy - Final kinetic energy
Loss in kinetic energy = 22,500 J - 10,000 J
Loss in kinetic energy = 12,500 J

Therefore, the loss in kinetic energy of the system just after the car has started moving is 12,500 J.

3. The impulse in the rope when it jerks the car into motion can be calculated using the equation:

impulse = change in momentum

The initial momentum of the system is 15,000 kg·m/s (as calculated in the first part), and the final momentum of the system is 0 (since the car was initially at rest and then starts moving). Therefore, the change in momentum is:

change in momentum = final momentum - initial momentum
change in momentum = 0 kg·m/s - 15,000 kg·m/s
change in momentum = -15,000 kg·m/s

The impulse in the rope is equal to the change in momentum, so the impulse in the rope when it jerks the car into motion is -15,000 kg·m/s.

(Note: The negative sign indicates that the impulse acts in the opposite direction of the initial momentum.)

To find the answers to the given questions, we'll make use of the laws of conservation of momentum and conservation of energy.

1. Find the speed of the tractor immediately the rope becomes taut:
Before the rope becomes taut, the tractor is moving with a speed of 3.0 m/s. Since the rope becomes taut, the system consisting of the tractor and the car will move together as a single entity.

According to the law of conservation of momentum, the total momentum before the rope becomes taut is equal to the total momentum after the rope becomes taut.

Total momentum before = Total momentum after

(mass of tractor × velocity of tractor) + (mass of car × velocity of car) = (mass of tractor + mass of car) × velocity of the combined system

The mass of the tractor is 5.0 × 10^3 kg, the mass of the car is 2.5 × 10^3 kg, and the velocity of the tractor is 3.0 m/s. We'll assume that initially, the velocity of the car is zero since it hasn't started moving yet.

(5.0 × 10^3 kg × 3.0 m/s) + (2.5 × 10^3 kg × 0 m/s) = (5.0 × 10^3 kg + 2.5 × 10^3 kg) × velocity of the combined system

Simplifying the equation:

(15.0 × 10^3 kg·m/s) = (7.5 × 10^3 kg) × velocity of the combined system

Dividing both sides by (7.5 × 10^3 kg):

velocity of the combined system = (15.0 × 10^3 kg·m/s) / (7.5 × 10^3 kg)

velocity of the combined system = 2.0 m/s

Therefore, the speed of the tractor immediately after the rope becomes taut is 2.0 m/s.

2. Loss in kinetic energy of the system just after the car has started moving:
To find the loss in kinetic energy of the system, we need to calculate the initial kinetic energy of the system before the car starts moving and the final kinetic energy of the system after the car starts moving.

The initial kinetic energy of the system is given by:

Initial kinetic energy = (1/2) × (mass of tractor + mass of car) × (velocity of the combined system)^2

Substituting the values:

Initial kinetic energy = (1/2) × (7.5 × 10^3 kg) × (3.0 m/s)^2

Initial kinetic energy = 33,750 J

The final kinetic energy of the system after the car starts moving is given by:

Final kinetic energy = (1/2) × (mass of tractor + mass of car) × (final velocity of the combined system)^2

Since the final velocity of the combined system is 2.0 m/s:

Final kinetic energy = (1/2) × (7.5 × 10^3 kg) × (2.0 m/s)^2

Final kinetic energy = 15,000 J

Therefore, the loss in kinetic energy of the system is:

Loss in kinetic energy = Initial kinetic energy - Final kinetic energy

Loss in kinetic energy = 33,750 J - 15,000 J

Loss in kinetic energy = 18,750 J

So, the loss in kinetic energy of the system just after the car has started moving is 18,750 J.

3. Impulse in the rope when it jerks the car into motion:
The impulse is defined as the change in momentum of an object. In this case, the impulse in the rope is equal to the change in the momentum of the car.

The change in momentum of the car can be calculated using the formula:

Impulse = (mass of car) × (final velocity of the car - initial velocity of the car)

The initial velocity of the car is 0 m/s (since it hasn't started moving yet) and the final velocity of the car is the velocity of the combined system, which we found to be 2.0 m/s.

Impulse = (2.5 × 10^3 kg) × (2.0 m/s - 0 m/s)

Impulse = 5,000 kg·m/s

Therefore, the impulse in the rope when it jerks the car into motion is 5,000 kg·m/s.