A small, 200 g cart is moving at 1.50 m/s on an air track when it collides with a larger, 2.00 kg cart at rest. After the collision, the small cart recoils at 0.890 m/s.
Q: What is the speed of the large cart after the collision?
How do you set this up? Would it be like (mass of small cart)/(mass of large cart)*1.50m/s? but then how do you use the 0.890 m/s?
Well, well, well, it seems we have ourselves a little collision dilemma. Don't worry, I've got just the solution for you. Let's dive into the physics playground and set this up.
First things first, we need to understand the conservation of momentum. Now, momentum is like that giant boulder rolling down a hill, it doesn't just disappear into thin air. It stays constant. So, before and after the collision, the total momentum of the system should remain the same.
The momentum formula is like the secret handshake for this problem. It's mass times velocity. So, let's start by finding the momentum of the small cart before the collision. That would be the mass of the small cart (200 g) times its initial velocity (1.50 m/s). Got it?
Now, the momentum after the collision should be the mass of the small cart (200 g) times its final velocity (0.890 m/s). See where we're going with this?
Now comes the part where the big cart steals the spotlight. Since the total momentum stays the same, we need to figure out how much momentum the big cart gained from the small cart. To do that, we subtract the momentum after the collision (that we just calculated) from the momentum before the collision (which was the momentum of the small cart only).
Now, to find the velocity of the large cart, we divide the momentum gained by the mass of the big cart (2.00 kg) and voila! We have the answer right in our hands.
So, to sum it all up:
Momentum before collision = (mass of small cart) * (initial velocity of small cart)
Momentum after collision = (mass of small cart) * (final velocity of small cart)
Momentum gained by big cart = Momentum before collision - Momentum after collision
Velocity of big cart = Momentum gained by big cart / (mass of big cart)
Now, it's time for you to crunch those numbers and find the speed of that big cart after the collision. Happy calculating!
To determine the speed of the large cart after the collision, you can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by its mass multiplied by its velocity. In this case, the momentum before the collision is the sum of the momenta of the small cart (200 g) and the large cart (2.00 kg), and the momentum after the collision is the sum of the momenta of the small cart and the large cart. We can assume that the positive direction is to the right.
Before the collision:
Momentum of small cart = (mass of small cart) * (velocity of small cart)
Momentum of large cart = (mass of large cart) * (velocity of large cart)
Total momentum before collision = (momentum of small cart) + (momentum of large cart)
After the collision:
Momentum of small cart = (mass of small cart) * (recoil velocity of small cart)
Momentum of large cart = (mass of large cart) * (velocity of large cart)
Total momentum after collision = (momentum of small cart) + (momentum of large cart)
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up the equation:
(momentum of small cart before collision) + (momentum of large cart before collision) = (momentum of small cart after collision) + (momentum of large cart after collision)
(mass of small cart) * (velocity of small cart) + (mass of large cart) * (velocity of large cart) = (mass of small cart) * (recoil velocity of small cart) + (mass of large cart) * (velocity of large cart)
The initial velocity of the large cart is 0 m/s because it is at rest. The only unknown in this equation is the final velocity of the large cart.
Now, substitute the given values:
(0.2 kg) * (1.50 m/s) + (2.00 kg) * (0 m/s) = (0.2 kg) * (0.890 m/s) + (2.00 kg) * (velocity of large cart)
Simplifying the equation:
0.3 kg·m/s = 0.178 kg·m/s + (2.00 kg) * (velocity of large cart)
Rearranging the equation:
(2.00 kg) * (velocity of large cart) = 0.3 kg·m/s - 0.178 kg·m/s
(2.00 kg) * (velocity of large cart) = 0.122 kg·m/s
Finally, divide both sides of the equation by the mass of the large cart (2.00 kg) to solve for the velocity of the large cart:
velocity of large cart = 0.122 kg·m/s / (2.00 kg)
velocity of large cart ≈ 0.061 m/s
Therefore, the speed of the large cart after the collision is approximately 0.061 m/s.
Assume linear momentum is conserved.
0.2*1.50 = 0.2*(-0.89) + 2.0*V
0.30 + 1.78 = 2.0 V
V = 1.04 m/s
Start with the law of conservation of momentum:
initial momentum=final momentum
200(1.5)+0=200(-.890)+2000*V
solve for V.