Two trolleys are moving in the same direction along a track. Trolley 1 has a momentum of 2 kg m/s and Trolley 2 has a momentum of 6 kg m/s. Trolley 2 catches up to Trolley 1. They collide, stick together and move off with a velocity of 2 m/s. Use the principle of conservation of momentum to work out the combined mass of the trolleys.
Question
Two trolleys are moving in the same direction along a track. Trolley 1 has a momentum of 2 kg m/s and Trolley 2 has a momentum of 6 kg m/s. Trolley 2 catches up to Trolley 1. They collide, stick together and move off with a velocity of 2 m/s. Use the principle of conservation of momentum to work out the combined mass of the trolleys.
Solution
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision.
Before the collision, the total momentum is the sum of the momentum of Trolley 1 and Trolley 2. So, the total momentum before the collision is 2 kg m/s (Trolley 1) + 6 kg m/s (Trolley 2) = 8 kg m/s.
After the collision, the two trolleys stick together and move off with a velocity of 2 m/s. We can use the formula for momentum (momentum = mass x velocity) to find the combined mass of the trolleys.
We know that the total momentum after the collision is also 8 kg m/s (from the conservation of momentum), and the velocity is 2 m/s. So, we can set up the equation:
8 kg m/s = mass x 2 m/s
To solve for mass, we divide both sides of the equation by 2 m/s:
mass = 8 kg m/s ÷ 2 m/s = 4 kg
So, the combined mass of the trolleys is 4 kg.
Similar Questions
Two carts with masses of 4.40 kg and 2.68 kg move toward each other on a frictionless track with speeds of 5.14 m/s and 3.04 m/s respectively. The carts stick together after colliding head-on. Find the final speed.
A car of mass 2000 kg which is travelling at 10 m/s crashes into a car of the same mass which is travelling at 5 m/s in the same direction. Calculate the total momentum of both cars after the collision.10,000 kg m/s40,000 kg m/s20,000 kg m/s30,000 kg m/s2A toy train of mass 0.5 kg which is travelling at 0.5 m/s crashes into a train of mass 1.0 kg which is travelling at 0.25 m/s in the opposite direction. Upon colliding, the trains stick together. Calculate their final velocity.0.5 m/s0.33 m/s0.17 m/s0 m/s3A car of mass 1500 kg which is travelling at 10 m/s is involved in a head-on collision with a car of mass 2000 kg which is travelling at 8 m/s. Upon colliding with one another, both cars stick together. With what velocity (magnitude and direction) will they move after the collision?8.86 m/s (in the direction in which the 2000 kg car was originally travelling)0.29 m/s (in the direction in which the 2000 kg car was originally travelling)8.86 m/s (in the direction in which the 1500 kg car was originally travelling)0.29 m/s (in the direction in which the 1500 kg car was originally travelling)4An airplane of mass 50,000 kg accelerates along a runway from rest to a velocity of 100 m/s in 20 seconds. Calculate the average resultant force which was acting on the plane during this time.100,000,000 N250,000 N0.04 N10,000 N5Which of the following is equal to the average resultant force which acts on an object while it is accelerating (or decelerating)?Its change in momentum multiplied by the time for which the force was actingThe time for which the force was acting divided by its change in momentumIts rate of change of momentum (its change in momentum divided by the time for which the force was acting)Its change in momentum (the difference between its initial and final momenta)6The action of a resultant force of 5 kN causes the momentum of a lorry to increase from 100,000 to 120,000 kg m/s. For how long was this resultant force acting on the lorry?44 seconds4 seconds24 seconds20 seconds
Object 1 has a velocity of 3 m/s and a mass of 5 kg. Object 2 also has a mass of 5 kg but isn't moving. Object 1 collides with Object 2 and they move off together. Work out their velocity using the principle of conservation of momentum.
1. A 4,500 kg railway train moves east at a velocity of 5 m/s on a level frictionless track when it collides with a stationary 6,500 kg coach train. If the two trains lock together upon impact, how fast do they move after collision?2. A 945 kg car moves to the right at a velocity of 18 m/s collides with a stationary truck of unknown mass. The two vehicles stick together and move off at a velocity of 7 m/s. What is the mass of the truck
A car and a bus are driving along a road at the same speed. The bus has twice the mass of the car. Which vehicle has the greater momentum?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.