Two sleds collide and stick together sled a has mass of 140kg and a speed of 17m/s sled b has a mass of 80kg and a speed of 24m/s. There is no friction between the sleds and snow. Will the sleds be motionless after the collision or which one will move the other
To determine whether the sleds will be motionless after the collision, or which one will move the other, we need to apply the principle of conservation of momentum.
The principle of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant before and after a collision.
Mathematically, the momentum of an object can be calculated by multiplying its mass (m) by its velocity (v). The total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
Total momentum = (mass of sled A * velocity of sled A) + (mass of sled B * velocity of sled B)
After the collision, the sleds stick together, so they will have the same final velocity (let's call it v'). Using the conservation of momentum, we can set up the equation:
Total momentum after collision = (total mass of sleds) * v'
To solve for v', we can equate the expressions for the total momentum before and after the collision:
(mass of sled A * velocity of sled A) + (mass of sled B * velocity of sled B) = (total mass of sleds) * v'
Substituting the given values:
(140 kg * 17 m/s) + (80 kg * 24 m/s) = (140 kg + 80 kg) * v'
Simplifying the equation:
(2380 kg·m/s) + (1920 kg·m/s) = (220 kg) * v'
4300 kg·m/s = (220 kg) * v'
Dividing both sides by (220 kg):
v' = (4300 kg·m/s) / (220 kg)
v' = 19.55 m/s (approximately)
Since the final velocity (v') is not zero, it means that the sleds will still be in motion after the collision. The direction of their motion will depend on the masses and velocities of the individual sleds. However, sled B with a higher mass and velocity will influence the movement of both sleds more than sled A.