A pickup truck (2268 kg) and a compact car (1100 kg) have the same momentum.
If the same horizontal net force were exerted on both vehicles, pushing them from rest over the same distance, what is the ratio of their final kinetic energies? (ratio: truck to car)
Thanks man. I sorta figured out the hard way.
(mt)(at) = (mc)(ac)
at / ac = mc / mt
a = (vf² - vi²)/ 2∆x
at / ac = (vt² / 2∆x) / (vc² / 2∆x)
at / ac = vt² / vc²
mc / mt = vt² / vc² = 1100/2268
KE-t / KE-c = (mt)(vt²) / (mc)(ct²)
KE-t / KE-c = mt / mc * vt² / vc²
KE-t / KE-c = 2268/1100 * 1100/2268 = 1
sigh...
To find the ratio of the final kinetic energies of the pickup truck and the compact car, we need to calculate their individual final kinetic energies.
Let's begin by calculating the final velocities of both vehicles using the principle of conservation of momentum. According to this principle, the total momentum before the force is applied should be equal to the total momentum after the force is exerted.
Given:
Mass of the pickup truck (m1) = 2268 kg
Mass of the compact car (m2) = 1100 kg
Initial velocities of both vehicles (u1 and u2) = 0 m/s (since they start from rest)
Using the equation for momentum (p = mv), the total momentum before the force is applied is:
Initial momentum of pickup truck (p1i) = m1 * u1 = 2268 kg * 0 m/s = 0 kg*m/s
Initial momentum of compact car (p2i) = m2 * u2 = 1100 kg * 0 m/s = 0 kg*m/s
Since the total momentum before and after the force is applied should be equal, the total momentum after the force is applied is also zero:
Total momentum after the force is applied (p1f + p2f) = 0 kg*m/s
The velocity of an object can be calculated using the equation p = mv, where p is momentum and m is mass. Rearranging the equation, we have v = p/m.
For the pickup truck:
Final velocity of the pickup truck (v1f) = p1f / m1 = 0 kg*m/s / 2268 kg = 0 m/s
For the compact car:
Final velocity of the compact car (v2f) = p2f / m2 = 0 kg*m/s / 1100 kg = 0 m/s
Since both vehicles have a final velocity of 0 m/s, their final kinetic energies will be equal to 0 J.
Therefore, the ratio of their final kinetic energies is 0:0, which can be simplified to 0.
work done = F * distance
in this case the work done goes straight into increasing the kinetic energy
F * d = increase in Ke
same for both
one to one
the end.