a 1500kg car travelling east with a speed of 20m/s collides at an intesection with a 2500kg van travelling south at a speed of 15m/s.The vehicle undergoes a perfectly inelastic collision, and the wreckage slides 6m before coming to rest.Find the magnitude and direction of the constant force that has decelerated them. force=ma
To find the magnitude and direction of the constant force that decelerated the vehicles, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. The initial momentum of the car can be calculated as follows:
Initial momentum of the car = mass of the car × velocity of the car
= 1500 kg × 20 m/s
= 30000 kg·m/s (east)
Similarly, the initial momentum of the van can be calculated as:
Initial momentum of the van = mass of the van × velocity of the van
= 2500 kg × (-15 m/s) (note: negative sign indicates south direction)
= -37500 kg·m/s (south)
Since the vehicles undergo a perfectly inelastic collision, they stick together after the collision and move as one. Let's denote the final velocity of the wreckage (car and van together) as 'v'.
The final momentum of the wreckage can be calculated by considering the mass of the wreckage (sum of the masses of the car and van) times the final velocity:
Final momentum of the wreckage = (mass of the car + mass of the van) × v
We know that the wreckage slides 6m before coming to rest, so the final velocity 'v' is 0 m/s.
Final momentum of the wreckage = (mass of the car + mass of the van) × 0
= 0 kg·m/s
According to the principle of conservation of momentum, the initial momentum of the vehicles should be equal to the final momentum of the wreckage:
Initial momentum of the car + Initial momentum of the van = Final momentum of the wreckage
30000 kg·m/s (east) + (-37500 kg·m/s) (south) = 0 kg·m/s
Now, to find the magnitude and direction of the force that decelerated the vehicles, we can use Newton's second law of motion, which states that force = mass × acceleration (F = ma).
Since the wreckage comes to rest, we can assume it experiences uniform deceleration before coming to rest over a distance of 6m. Let's denote the deceleration as 'a'.
The final velocity 'v' can be calculated using the equation of motion: v² = u² + 2as, where u is the initial velocity (20 m/s for the car).
0² = 20² + 2a × 6
0 = 400 + 12a
12a = -400
a = -400 / 12
a = -33.33 m/s² (negative sign indicates deceleration)
Now we can find the magnitude of the force using Newton's second law: force = mass × acceleration
For the wreckage, mass = mass of the car + mass of the van = 1500 kg + 2500 kg = 4000 kg
Force = mass × acceleration
= 4000 kg × (-33.33 m/s²)
= -133,320 N
Therefore, the magnitude of the constant force that decelerated the vehicles is approximately 133,320 Newtons (N). The negative sign indicates that the force acted in the opposite direction of the initial motion.
To find the direction of the force, we can use the direction of the initial motion, which is east for the car. Therefore, the direction of the constant force that decelerated the vehicles is west.