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QuestionA 2 kg2 \mathrm{~kg} toy train at 1.25 m/s1.25 \mathrm{~m/s} collides with a stationary 0.5 kg0.5 \mathrm{~kg} train. Find their speed post-collision.

Studdy Solution

STEP 1

Assumptions1. The mass of the moving toy train is kg. The speed of the moving toy train is1.25 m/s3. The mass of the stationary toy train is0.5 kg4. After the collision, the two toy trains connect together and move as one object5. The law of conservation of momentum applies, which states that the total momentum before the collision is equal to the total momentum after the collision

STEP 2

First, we need to calculate the initial momentum before the collision. The momentum of an object is calculated by multiplying its mass by its velocity.
Initial momentum=Massmoving traintimesVelocitymoving train+Massstationary traintimesVelocitystationary trainInitial\, momentum = Mass_{moving\, train} \\times Velocity_{moving\, train} + Mass_{stationary\, train} \\times Velocity_{stationary\, train}

STEP 3

Now, plug in the given values for the mass and velocity of the moving train and the mass of the stationary train (whose velocity is zero because it is stationary) to calculate the initial momentum.
Initial momentum=2 kgtimes1.25 m/s+0.5 kgtimes0 m/sInitial\, momentum =2\, kg \\times1.25\, m/s +0.5\, kg \\times0\, m/s

STEP 4

Calculate the initial momentum.
Initial momentum=2 kgtimes1.25 m/s+0 kg m/s=2. kg m/sInitial\, momentum =2\, kg \\times1.25\, m/s +0\, kg\, m/s =2.\, kg\, m/s

STEP 5

The total momentum after the collision is the same as the total momentum before the collision (due to the conservation of momentum). So, the final momentum is also2.5 kg m/s. This final momentum is the mass of the combined trains times their final velocity.
Final momentum=(Massmoving train+Massstationary train)timesFinal velocityFinal\, momentum = (Mass_{moving\, train} + Mass_{stationary\, train}) \\times Final\, velocity

STEP 6

Substitute the given values for the masses of the trains into the equation.
2.5 kg m/s=(2 kg+0.5 kg)timesFinal velocity2.5\, kg\, m/s = (2\, kg +0.5\, kg) \\times Final\, velocity

STEP 7

implify the equation.
2.5 kg m/s=2.5 kgtimesFinal velocity2.5\, kg\, m/s =2.5\, kg \\times Final\, velocity

STEP 8

olve for the final velocity.
Final velocity=2.5 kg m/s/2.5 kg=1 m/sFinal\, velocity =2.5\, kg\, m/s /2.5\, kg =1\, m/sThe two trains will continue moving at a speed of1 m/s after the collision.

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