A small, 300g cart is moving at 1.60m/s on an air track when it collides with a larger, 2.00kg cart at rest. After the collision, the small cart recoils at 0.820m/s.
What is the speed of the large cart after the collision?
Use conservation of momentum.
m1u1+m2u2 = m1v1+m2v2
Before collision
m1=0.30kg
u1=1.6 m/s
m2=2.00 kg
u2=0
after collision
v1=0.82 m/s
Solve for v2.
1.1
To find the speed of the large cart after the collision, we can use the law of conservation of momentum.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision is given by the product of the mass and the velocity:
momentum_before = (mass_small * velocity_small) + (mass_large * velocity_large)
After the collision, the small cart recoils at 0.820 m/s, so the velocity of the small cart after the collision is -0.820 m/s (negative sign indicates opposite direction of motion).
Now we can rearrange the equation to solve for the velocity of the large cart:
(velocity_large) = (momentum_before - (mass_small * velocity_small)) / mass_large
Substituting the given values:
mass_small = 0.300 kg
velocity_small = 1.60 m/s
mass_large = 2.00 kg
velocity_small_after_collision = -0.820 m/s
(velocity_large) = ((mass_small * velocity_small) - (mass_small * velocity_small_after_collision)) / mass_large
Let's calculate the value:
(velocity_large) = ((0.300 kg * 1.60 m/s) - (0.300 kg * -0.820 m/s)) / 2.00 kg
(velocity_large) = (0.480 kg·m/s + 0.246 kg·m/s) / 2.00 kg
(velocity_large) = 0.726 kg·m/s / 2.00 kg
(velocity_large) = 0.363 m/s
Therefore, the speed of the large cart after the collision is 0.363 m/s.
To find the speed of the large cart after the collision, we can apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided there are no external forces acting on the system.
The momentum of an object is calculated by multiplying its mass with its velocity. Mathematically, momentum (p) is given by:
p = m * v
Where p is the momentum, m is the mass, and v is the velocity.
Let's denote the mass of the small cart as m1, the velocity of the small cart before the collision as v1, the mass of the large cart as m2, the velocity of the large cart after the collision as v2.
According to the law of conservation of momentum:
m1 * v1 (momentum before the collision) = m1 * v1 (momentum after the collision) + m2 * v2
Plugging in the given values:
m1 = 0.3 kg (mass of small cart),
v1 = 1.6 m/s (velocity of small cart before the collision),
m2 = 2.0 kg (mass of large cart),
v2 = ? (velocity of large cart after the collision).
We can rearrange the equation to solve for v2:
m1 * v1 = m1 * v1 + m2 * v2
m1 * v1 - m1 * v1 = m2 * v2
0 = m2 * v2 - m1 * v1
m2 * v2 = m1 * v1
v2 = (m1 * v1) / m2
Plugging in the values:
v2 = (0.3 kg * 1.6 m/s) / 2.0 kg
Now we can calculate:
v2 = (0.48 kg*m/s) / 2.0 kg
v2 = 0.24 m/s
Therefore, the speed of the large cart after the collision is 0.24 m/s.