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^1 just before the towing rope became taut.calculate:the speed of the tractor immediately the rope became taut, loose kinetic energy of the system just after the car has started moving and the impulse in the rope when it jerk the car into motion.
Pls help answer the question
A ball of mass 5.0kg hit a smoth vertical wall normally with the same speed of 2m\s and respond with the same speed.Determine the impulse exprienced by the ball
HALP
To calculate the speed of the tractor immediately after the towing rope became taut, we can use the principle of conservation of momentum.
The initial momentum of the system (tractor + car) just before the rope becomes taut is given by:
Initial momentum = Mass of tractor * Speed of tractor + Mass of car * Speed of car
The final momentum of the system just after the rope becomes taut is given by:
Final momentum = (Mass of tractor + Mass of car) * Final speed
Since there is no external force acting on the system, the initial momentum and the final momentum should be equal.
Therefore, Mass of tractor * Speed of tractor + Mass of car * Speed of car = (Mass of tractor + Mass of car) * Final speed
Given:
Mass of tractor (m1) = 5.0 * 10^3 kg
Mass of car (m2) = 2.5 * 10^3 kg
Speed of tractor (v1) = 3.0 m/s
Speed of car (v2) = 0 m/s (car is not yet moving when the rope is taut)
Plugging in these values into the equation, we can solve for the final speed:
(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) * Final speed
Simplifying the equation:
15,000 kg·m/s = 17,500 kg * Final speed
Dividing both sides by 17,500 kg:
Final speed = 15,000 kg·m/s / 17,500 kg
Final speed = 0.857 m/s (rounded to three decimal places)
Therefore, the speed of the tractor immediately after the rope becomes taut is approximately 0.857 m/s.
To calculate the loose kinetic energy of the system just after the car has started moving, we can use the formula:
Loose Kinetic Energy = 1/2 * (Mass of tractor + Mass of car) * Final speed^2
Given:
Mass of tractor (m1) = 5.0 * 10^3 kg
Mass of car (m2) = 2.5 * 10^3 kg
Final speed (v) = 0.857 m/s (calculated in the previous step)
Substituting these values into the formula, we can calculate the loose kinetic energy:
Loose Kinetic Energy = 1/2 * (5.0 * 10^3 kg + 2.5 * 10^3 kg) * (0.857 m/s)^2
Calculating the loose kinetic energy:
Loose Kinetic Energy ≈ 1/2 * 7.5 * 10^3 kg * (0.857 m/s)^2
Loose Kinetic Energy ≈ 2,563.78 J (rounded to two decimal places)
Therefore, the loose kinetic energy of the system just after the car has started moving is approximately 2,563.78 J.
To calculate the impulse in the rope when it jerks the car into motion, we can use the impulse-momentum principle. The impulse is the change in momentum of the car.
Impulse = Final momentum - Initial momentum of the car
Given:
Mass of car (m2) = 2.5 * 10^3 kg
Speed of car (v2) = 0 m/s (initially at rest)
Final speed (v) = 0.857 m/s (calculated in the first step)
Initial momentum of the car = Mass of car * Speed of car (0 m/s)
Impulse = (Mass of car * Final speed) - (Mass of car * Speed of car)
Impulse = 2.5 * 10^3 kg * 0.857 m/s - 2.5 * 10^3 kg * 0 m/s
Simplifying the equation:
Impulse ≈ 2,142.5 kg·m/s (rounded to one decimal place)
Therefore, the impulse in the rope when it jerks the car into motion is approximately 2,142.5 kg·m/s.