A delivery truck with a mass of 1700 kg is stopped in the street w/o its brakes on, when a small car hits it from behind. The car has a mass of 650 kg, and is traveling at 3.7m/s immediately before it hits the truck. Both the car and the truck have good bumpers, so assume the collision is elastic.
Find the final velocity of the two vehicles. Consider the direction that the car was originally traveling to be the forward direction
Detailed solutions, with step by step instructions are greatly appreciated. THANK YOU!
YOu cant assume elasticity in this. THe brakes are on on the truck. What do you think brakes do? ANS: they absorb energy.
So the KE total cannot equal incoming energy, before the truck could ever move at all, the brakes are holding it, absorbing energy. Don't let the teacher convince you the truck gets an "initial velocity". It doesn't, if it moves, the brakes are absorbing energy.
thank you. but i don't think this is the answer they are looking for :(. hypothetically, can we assume elasticity?
oops, the it says w/0 the brakes. darn.
so you have two conditions:
a) conservation of momentum
intialmoment=final momentum
M*0+ m*3.7=MV' + mv'
now, conservation of energy.
1/2 m *3.7^2=1/2 M V'^2 + 1/2 mv'^2
two equations, two unknowns (V' and v')
To solve, start with the first equation, solve for one of the unknowns.
as in V'=(3.7m-mv')/M
now, the hard and messy part. Put numbers for m and M . then, put that expression in the second equation for V'
Yes, you have to square that term, so FOIL it.
after that, it is just algebra to solve for v', use the quadratic equation. Check both solutions, usually one of them will be the starting velocity as if it passed through the big mass (and V' of course is zero), ignore that solution.
Have fun.
thank you so much. i'll get working on this.
To find the final velocities of the truck and the car after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.
Step 1: Write down the given information:
- Mass of the truck (m1) = 1700 kg
- Mass of the car (m2) = 650 kg
- Initial velocity of the car (v2i) = 3.7 m/s
- Final velocities of the truck (v1f) and the car (v2f) are unknown.
Step 2: Calculate the initial momentum before the collision:
- Initial momentum of the truck (p1i) = m1 * 0 (since the truck is stopped) = 0
- Initial momentum of the car (p2i) = m2 * v2i
Step 3: Calculate the final momentum after the collision:
- Final momentum of the truck (p1f) = m1 * v1f
- Final momentum of the car (p2f) = m2 * v2f
Step 4: Apply the conservation of momentum:
- According to the conservation of momentum, the initial momentum of the system should be equal to the final momentum of the system.
- Therefore, p1i + p2i = p1f + p2f
Since the truck is initially at rest (v1i = 0), we can simplify the equation to:
m2 * v2i = m1 * v1f + m2 * v2f
Step 5: Solve the equation for the final velocities:
- Rearrange the equation to solve for v1f:
v1f = (m2 * v2i - m2 * v2f) / m1
- Rearrange the equation to solve for v2f:
v2f = (m2 * v2i - m1 * v1f) / m2
Substitute the given values into the equations and solve for the final velocities.
Please note that in an elastic collision, both kinetic energy and momentum are conserved.