A 0.400-kg toy truck moving at an initial speed of 0.100 m/s collides head-on with a 0.300-kg toy car at rest. The collision is perfectly inelastic, so the two toys stick together. a)Find their final speed? b)Calculate how much kinetic energy was lost in the collision?
2006-07-25 13:43:39 · 6 answers · asked by Lou 1 in Science & Mathematics ➔ Mathematics
KE = 1/2 m v^2
Before collision truck KE = 1/2 (0.400 kg)(0.100 m/s)^2 = ?
before collision car KE = 1/2 (0.300 kg)(0.00 m/s)^2 = 0 j
After collision truck + car KE = 1/2 (0.700 kg)(? m/s)^2
The KE of the system before the collision will equal the KE of the system after the collision. So the KE of the truck + KE of the car (o) = total before collision.
That means that the KE of the truck + car after the collision is the same as the truck before. Substitue this into the equation and calculate the velocity of the two after the collision.
2006-07-25 13:52:50 · answer #1 · answered by physandchemteach 7 · 0⤊ 0⤋
As the collision is inelastic, the speed after the collision is given by the total momentum before the collision divided by the total mass. So if m,m' are the masses and u,u' are the velocities then the final velocity is (mu+m'u')/(m+m'). In this problem m = 0.4, m' = 0.3, u = 0.1 and u' = 0 so the final velocity is (0.4x0.1)/0.7 = 0.057...m/s.
To find the loss of KE, note that the toy car has no KE before impact so the KE before impact is (0.5)x(0.4)x[(0.1)^2]=0.002 and after impact we have a 0.7kg mass moving at 0.057...m/s so the KE is (0.5)x (0.7)x (0.057...)^2 = 0.0011429 and the loss is 0.000857... units.
Note that there is a useful formula for the loss of KE in a collision. It is
(1/2)mm' (1-e^2)[(u-u' )^2]/(m+m' ),
where e is the coefficient of restitution which is zero for an inelastic collision. Thus for an inelastic collision, the loss of KE is given by (1/2)mm' [(u-u' )]^2/(m+m' ). If you substitute the values into this expression you will arrive at the same answer as given above.
2006-07-25 21:57:26 · answer #2 · answered by grsym 2 · 0⤊ 0⤋
Hint: use conservation of momentum
PhysandChemTeach is mistaken. Kinetic energy is not conserved in an inelastic collison.
2006-07-25 20:57:13 · answer #3 · answered by Demiurge42 7 · 0⤊ 0⤋
speed=.4/7
lost kinetic energy=.06/7
2006-07-26 02:02:48 · answer #4 · answered by Anonymous · 0⤊ 0⤋
That's physics, not mathematics
2006-07-25 21:10:44 · answer #5 · answered by Blues Man 2 · 0⤊ 0⤋
physics sucks. read the textbook for answers, cheater.
2006-07-25 20:49:57 · answer #6 · answered by nickname 1 · 0⤊ 1⤋