A small, 300 g cart is moving at 1.90 m/s on an air track when it collides with a larger, 2.00 g cart at rest. After the collision, the small cart recoils at 0.820 m/s. What is the speed of the large cart after the collision?
You will have to use conservation of momentum
Momentum1+Momentum2=momentum1'+momentum2'
300*1.90+0=300(-.820)+Massother*V
You list the other as "larger" 2g..which is not larger. At any rate, solve for v2'
To solve this problem, we can apply the principles of conservation of momentum.
The law of conservation of momentum states that the total momentum of a system remains constant before and after a collision, as long as no external forces are acting on the system.
The momentum of an object is defined as the product of its mass and velocity, and it is a vector quantity. The symbol for momentum is p.
Before the collision, the momentum of the small cart is given by:
m1 * v1 = (0.300 kg) * (1.90 m/s) = 0.57 kg*m/s (equation 1)
Where m1 represents the mass of the small cart and v1 represents its initial velocity.
Since the larger cart is at rest, its initial momentum is zero:
m2 * v2 = 0 (equation 2)
Where m2 represents the mass of the large cart and v2 represents its initial velocity.
After the collision, the small cart recoils with a velocity of 0.820 m/s. The momentum of the small cart is then:
m1 * v1' = (0.300 kg) * (0.820 m/s) = 0.246 kg*m/s (equation 3)
Where v1' represents the final velocity of the small cart.
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. That is:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2' (equation 4)
Where v2' represents the final velocity of the large cart.
Substituting the values we have:
0.57 kg*m/s + 0 kg*m/s = 0.246 kg*m/s + m2 * v2'
Simplifying the equation:
0 = 0.246 kg*m/s + m2 * v2'
Rearranging the equation to solve for v2':
m2 * v2' = -0.246 kg*m/s
Now, since the velocity must be a positive value, we can remove the negative sign:
m2 * v2' = 0.246 kg*m/s
Finally, solving for v2':
v2' = 0.246 kg*m/s / m2
Given that the mass of the larger cart is 2.00 kg, we can substitute this value:
v2' = 0.246 kg*m/s / 2.00 kg
Calculating this expression gives us:
v2' = 0.123 m/s
Therefore, the speed of the larger cart after the collision is 0.123 m/s.