A 910 kg sports car slows down to 6.0 m/s to read a cross street sign. The 1440 kg pick-up truck following the sports car fails to see that the sports car has slowed and continues traveling at 17.0 m/s. The pick-up slams into the sports car. With what velocity will the two move, if they lock bumpers after the rear end collision? Assume both cars are traveling north and north is the positive direction
I tried find the change in momentum between the two cars then equating that momentum with both mass together and solved for the final velocity but i got it wrong.
M1 = 910kg*6m/s = 5460kg-m/s
M2 = 1440kg*17/s = 24480kg-m/s
Mt = M1+M2 = 5460+24480 = 29940 kg-m/s
Masstot = 910 + 1440 = 2350kg
V = Mt/Masstot = 29940/2350 = 12.74 m/s
To solve this problem, you need to apply the principle of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision.
First, let's calculate the initial momentum of each car before the collision:
Momentum of the sports car (Car 1):
Initial mass of the sports car (m1) = 910 kg
Initial velocity of the sports car (v1) = 6.0 m/s
Initial momentum of the sports car (p1) = m1 * v1
Momentum of the pick-up truck (Car 2):
Initial mass of the pick-up truck (m2) = 1440 kg
Initial velocity of the pick-up truck (v2) = 17.0 m/s
Initial momentum of the pick-up truck (p2) = m2 * v2
Now, let's calculate the total initial momentum (before the collision):
Initial total momentum (Pi) = p1 + p2
Next, according to the principle of conservation of momentum, the total momentum after the collision (Pf) should be equal to the initial total momentum (Pi):
Final total momentum (Pf) = Pi
Since the two cars lock bumpers after the collision, the final velocities of both cars will be the same. Let's denote the final velocity of both cars as Vf.
So, the final momentum of the sports car (Car 1) will be:
Final momentum of the sports car (pf1) = (m1 + m2) * Vf
The final momentum of the pick-up truck (Car 2) will also be:
Final momentum of the pick-up truck (pf2) = (m1 + m2) * Vf
Now, equating the final total momentum (Pf) with the sum of the final momenta of both cars (pf1 + pf2), we get:
Pi = pf1 + pf2
Pi = (m1 + m2) * Vf + (m1 + m2) * Vf
Pi = 2 * (m1 + m2) * Vf
Now, solving for Vf:
Vf = Pi / (2 * (m1 + m2))
Plug in the values of the initial momenta (p1 and p2), the masses (m1 and m2), and solve for Vf.
Substituting the given values:
Pi = p1 + p2
Pi = (910 kg * 6.0 m/s) + (1440 kg * 17.0 m/s)
Calculate Pi, then substitute the values into the equation and solve for Vf to find the final velocity of the two cars after the collision.