HI. Can someone please help me with this question.
Two identical cars hit each other and lock bumpers. In each of the following cases, what are the speeds of the cars immediately after coupling bumpers? (a) A car moving with a speed of 90 km/h approaches a stationary car; (b) two cars approach each other with speeds of 90 km/h and 120 km/h, respectively; (c) two cars travel in the same direction with speeds of 90 km/h and 120 km/h, respectively.
These are all conservation of momentum problems, but easy because the cars stick together after the crash so the final mass is (2m)and they are both at the same final speed v
so
m u1 + m u2 = 2m v
or
u1 + u2 = 2v for all cases
for example for part b
u1 = 90
u2 = -120
so for part b
90 - 120 = 2 v
v = -15 answer for part b
You should be able to do parts a and c now.
Certainly! I'd be happy to help you with this physics question.
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision. Momentum is defined as the product of an object's mass and its velocity.
Let's break down each case one by one:
(a) A car moving with a speed of 90 km/h approaches a stationary car.
In this scenario, since one car is stationary, its initial velocity is 0 km/h. The other car is moving with a speed of 90 km/h. Since the cars have identical masses, their masses cancel out when computing momentum. Therefore, the total momentum before the collision is (mass of car 1 × velocity of car 1) + (mass of car 2 × velocity of car 2) = (m × 90 km/h) + (m × 0 km/h) = m × 90 km/h.
Since the cars get locked together after the collision, they move with the same final velocity. Let's call this final velocity "v". According to the principle of conservation of momentum, the total momentum after the collision is also m × v.
Setting the initial and final momenta equal, we can write:
m × 90 km/h = m × v
Canceling out the mass:
90 km/h = v
So the final velocity of the two cars after coupling is 90 km/h in the direction of the initial moving car.
(b) Two cars approach each other with speeds of 90 km/h and 120 km/h, respectively.
In this case, the cars have different initial velocities. Let's call the initial velocity of car 1 as "v1" (90 km/h) and the initial velocity of car 2 as "v2" (120 km/h). Again, since the cars have identical masses, their masses cancel out when computing momentum.
The total momentum before the collision is (mass of car 1 × velocity of car 1) + (mass of car 2 × velocity of car 2) = (m × 90 km/h) + (m × (-120) km/h) = m × (-30) km/h.
Note that we take the negative sign for the velocity of car 2 because it's moving in the opposite direction.
As the cars get locked together after the collision, they move with the same final velocity "v." According to the principle of conservation of momentum, the total momentum after the collision is also m × v.
Setting the initial and final momenta equal, we have:
m × (-30) km/h = m × v
Canceling out the mass:
-30 km/h = v
So the final velocity of the two cars after coupling is -30 km/h. The negative sign indicates that the cars move in the opposite direction of the initial velocity of car 2.
(c) Two cars travel in the same direction with speeds of 90 km/h and 120 km/h, respectively.
In this case, the cars have the same initial direction and thus the same sign in their velocities. Let's call the initial velocity of car 1 as "v1" (90 km/h) and the initial velocity of car 2 as "v2" (120 km/h). Again, since the cars have identical masses, their masses cancel out when computing momentum.
The total momentum before the collision is (mass of car 1 × velocity of car 1) + (mass of car 2 × velocity of car 2) = (m × 90 km/h) + (m × 120 km/h) = m × 210 km/h.
As the cars get locked together after the collision, they move with the same final velocity "v." According to the principle of conservation of momentum, the total momentum after the collision is also m × v.
Setting the initial and final momenta equal, we have:
m × 210 km/h = m × v
Canceling out the mass:
210 km/h = v
So the final velocity of the two cars after coupling is 210 km/h, in the direction of their initial motion.