A 3,0kg cart moving East with a speed of 1.0ms^-1 collides head-on with a 5.0 kg cart that is initially moving West with a speed of 2.0 m.s^-1. After the collision, then 3.0 kg cart is moving to the left with a speed of 1.0 m.s^-1. IGNORE THE FRICTION, WHAT IS FINAL VELOCITY OF 5.0KG CART?
initial momentum east
= 3 * 1 - 5 * 2 = -7
so final momentum east = -7
I guess left is west, negative
-7 = 3 * -1 + 5 * u
5 u = -4
u = 4/5 west
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
Let's define the positive direction as east and rightwards. We can see that both carts are initially moving in opposite directions.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
The total momentum before the collision can be calculated as:
Total momentum before collision = (mass of 3.0 kg cart × velocity of 3.0 kg cart) + (mass of 5.0 kg cart × velocity of 5.0 kg cart)
= (3.0 kg × 1.0 m/s) + (5.0 kg × (-2.0 m/s))
= 3.0 kg⋅m/s - 10.0 kg⋅m/s
= -7.0 kg⋅m/s
Since momentum is conserved, the total momentum after the collision should also be -7.0 kg⋅m/s.
Now, let's assume the final velocity of the 5.0 kg cart is V. Since it is moving in the left direction, its velocity will be negative:
Total momentum after collision = (mass of 3.0 kg cart × velocity of 3.0 kg cart) + (mass of 5.0 kg cart × velocity of 5.0 kg cart)
= (3.0 kg × (-1.0 m/s)) + (5.0 kg × V)
Using the conservation of momentum principle, we have:
Total momentum before collision = Total momentum after collision
-7.0 kg⋅m/s = (3.0 kg × (-1.0 m/s)) + (5.0 kg × V)
Simplifying the equation:
-7.0 kg⋅m/s = -3.0 kg⋅m/s + 5.0 kg⋅V
Subtracting -3.0 kg⋅m/s from both sides:
-4.0 kg⋅m/s = 5.0 kg⋅V
Dividing both sides by 5.0 kg:
-0.8 m/s = V
Therefore, the final velocity of the 5.0 kg cart is -0.8 m/s to the left (westward).
To find the final velocity of the 5.0 kg cart after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass with its velocity. So, let's calculate the initial momentum:
Initial momentum of the 3.0 kg cart = mass * velocity
= 3.0 kg * 1.0 m/s
= 3.0 kg m/s
Initial momentum of the 5.0 kg cart = mass * velocity
= 5.0 kg * (-2.0 m/s) [since the velocity is in the opposite direction]
= -10.0 kg m/s
Now, let's calculate the final momentum:
Final momentum of the 3.0 kg cart = mass * velocity
= 3.0 kg * (-1.0 m/s) [since the velocity is to the left]
= -3.0 kg m/s
Let's assume the final velocity of the 5.0 kg cart is v.
Final momentum of the 5.0 kg cart = mass * velocity
= 5.0 kg * v
= 5v kg m/s
According to the conservation of momentum principle, the total momentum before the collision should be equal to the total momentum after the collision. Therefore, we can write:
Initial momentum of the 3.0 kg cart + Initial momentum of the 5.0 kg cart = Final momentum of the 3.0 kg cart + Final momentum of the 5.0 kg cart
(3.0 kg m/s) + (-10.0 kg m/s) = (-3.0 kg m/s) + (5v kg m/s)
-7.0 kg m/s = -3.0 kg m/s + 5v kg m/s
Simplifying the equation:
-7.0 kg m/s + 3.0 kg m/s = 5v kg m/s
-4.0 kg m/s = 5v kg m/s
Dividing both sides of the equation by 5 kg m/s:
-0.8 m/s = v
Therefore, the final velocity of the 5.0 kg cart is -0.8 m/s or in other words, it is moving to the left with a speed of 0.8 m/s.