In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity. It was then allowed to collide with a second body B, which was initially at rest and the bodies moved off together at constant velocity. The following data were recorded. Mass of body A = 125.6 g Mass of body B = 111.1 g Distance travelled by body A for 0.2 s before collision = 11.4 cm Distance travelled by bodies A and B for 0.2 s after collision = 6.1 cm (i) Draw a labelled diagram of how the apparatus was arranged in this experiment. (ii) Describe how the time interval was measured. (iii) How were the effects of (a) friction and (b) gravity minimised? (iv) Use the data to calculate the initial and final velocities of body A, (v) demonstrate how the experiment verifies the principle of conservation of momentum.

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In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity - Leaving Cert Physics - Question 1 - 2020

Question 1

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In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity. It was then allowed to collide with a second... show full transcript

Worked Solution & Example Answer:In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity - Leaving Cert Physics - Question 1 - 2020

Step 1

Draw a labelled diagram of how the apparatus was arranged in this experiment.

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Answer

The apparatus consists of two trolleys on a smooth track. Body A is attached to one trolley, while body B is on another trolley. Both trolleys are positioned at one end of the track with a light gate placed along the track to measure the time interval. An air cushion may be used underneath to minimize friction.

Step 2

Describe how the time interval was measured.

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Answer

The time interval was measured using a light gate. The number of gaps in the light gate is quantified, and the time taken for a rider to pass through can be calculated using the formula:

$ext{Time} = ext{Number of gaps} imes 0.02 ext{ s}$

Step 3

How were the effects of (a) friction and (b) gravity minimised?

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Answer

(a) Friction was minimised by using a smooth air track or placing air cushions beneath the trolleys, reducing contact with the surface.

(b) Gravity was minimised by keeping the apparatus level and ensuring that the track is horizontal, thus preventing any acceleration due to gravity that could affect the motion of the trolleys.

Step 4

Use the data to calculate the initial and final velocities of body A.

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Answer

To find the initial velocity of body A, we use the distance travelled before collision:

$u = rac{ ext{Distance}}{ ext{Time}} = rac{11.4 ext{ cm}}{0.2 ext{ s}} = 57 ext{ cm/s} = 0.57 ext{ m/s}$

For the final velocity after the collision:

The distance travelled together by both bodies is 6.1 cm:

$v = rac{6.1 ext{ cm}}{0.2 ext{ s}} = 30.5 ext{ cm/s} = 0.305 ext{ m/s}$

Step 5

demonstrate how the experiment verifies the principle of conservation of momentum.

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Answer

To demonstrate the principle of conservation of momentum, we calculate the momentum before and after the collision.

The initial momentum of body A is:

$p_a = m_a imes u = 0.1256 ext{ kg} imes 0.57 ext{ m/s} = 0.072 ext{ kg m/s}$

The momentum after the collision of bodies A and B combined is:

$p_b = (m_a + m_b) imes v = (0.1256 + 0.1111) ext{ kg} imes 0.305 ext{ m/s} = 0.072 ext{ kg m/s}$

Since $p_b = p_a$ , the experiment verifies the conservation of momentum as both values are equal.

In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity - Leaving Cert Physics - Question 1 - 2020

Worked Solution & Example Answer:In an experiment to verify the principle of conservation of momentum, body A was set in motion with a constant velocity - Leaving Cert Physics - Question 1 - 2020

Draw a labelled diagram of how the apparatus was arranged in this experiment.

Describe how the time interval was measured.

How were the effects of (a) friction and (b) gravity minimised?

Use the data to calculate the initial and final velocities of body A.

demonstrate how the experiment verifies the principle of conservation of momentum.

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