A toy car mass 0.05 kg ,on a ramp with no friction , begins at 0.7 meters high. At the bottom it collides inelastically with a toy truck mass 0.2 kg, at rest. After the collision the car is at rest, what is the final velocity of the truck?
Ke of toy car =(1/2) m v^2 = m g h
so
v = sqrt(2gh) = sqrt(2*9.81*0.7)
v = 3.71 m/s
momentum = 0.05*v = 0.185 kg m/s
so
0.2 u = 0.185
u = 0.926 m/s
V^2 = Vo^2 + 2g*h.
V^2 = 0 + 19.6*0.7 = 13.72
V = 3.7 m/s = Velocity at the bottom of the ramp.
M1*V1 + M2*V2 = M1*0 + M2*V.
0.05*3.7 + M2*0 = 0 + 0.2V
0.185 = 0.2V
V = 0.925m/s = Final velocity of the truck.
To find the final velocity of the truck after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision in an isolated system.
The momentum of an object is given by the product of its mass and velocity.
Let's denote the initial velocity of the toy car as v1 and the final velocity of the truck as v2.
Since the toy car is at rest after the collision, its final velocity is 0 m/s (v1 = 0 m/s).
The momentum before the collision is given by the sum of the individual momenta of the toy car and the toy truck.
Initial momentum = (mass of car × velocity of car) + (mass of truck × velocity of truck)
0 = (0.05 kg × 0 m/s) + (0.2 kg × v2)
Simplifying the equation, we get:
0 = 0 + 0.2 kg × v2
0 = 0.2 kg × v2
Dividing both sides by 0.2 kg, we find:
0 = v2
Therefore, the final velocity of the truck after the collision is 0 m/s.
To find the final velocity of the truck after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision (car + truck) should be equal to the total momentum after the collision.
Before the collision:
The momentum of an object is given by the product of its mass and velocity.
For the car:
Momentum of the car = Mass of the car × Velocity of the car before the collision
Since the car is at rest initially, the velocity of the car before the collision is 0.
For the truck:
Momentum of the truck = Mass of the truck × Velocity of the truck before the collision
The truck is initially at rest, so the velocity of the truck before the collision is also 0.
The total momentum before the collision (car + truck) is given by:
Total momentum before collision = Momentum of the car + Momentum of the truck
After the collision:
Since the car and truck collide inelastically (stick together after the collision), they have a combined mass of 0.05 kg + 0.2 kg = 0.25 kg.
Since the car is at rest after the collision, its velocity is 0.
To find the final velocity of the truck after the collision, we can use the conservation of momentum principle.
According to the principle of conservation of momentum, the total momentum after the collision should be equal to the total momentum before the collision.
This can be written as:
Total momentum before collision = Total momentum after collision
Therefore:
(Momentum of the car before the collision + Momentum of the truck before the collision) = (Momentum of the car after the collision + Momentum of the truck after the collision)
Using the information we have:
(0 + 0) = (0 + Momentum of the truck after the collision)
Since the car and the truck are both initially at rest, the total momentum before the collision is 0. Therefore, the momentum of the truck after the collision is also 0.
Since momentum is given by the product of mass and velocity, the momentum of the truck after the collision is 0 only if its velocity is also 0. Hence, the final velocity of the truck after the collision is 0 m/s.