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04.1 State what is meant by an inertial frame of reference - AQA - A-Level Physics - Question 4 - 2021 - Paper 7
Question 4
04.1 State what is meant by an inertial frame of reference. 04.2 A pair of detectors is set up to measure the intensity of a parallel beam of unstable particles. In... show full transcript
Worked Solution & Example Answer:04.1 State what is meant by an inertial frame of reference - AQA - A-Level Physics - Question 4 - 2021 - Paper 7
Step 1
State what is meant by an inertial frame of reference.
Answer
An inertial frame of reference is defined as a frame of reference in which an object is either at rest or moving at a constant velocity. In this frame, Newton's laws of motion are valid, meaning that objects do not experience any acceleration unless acted upon by a net external force.
Step 2
Calculate the half-life of the particles in the reference frame in which they are at rest.
Answer
To find the half-life, we first determine the distance between the detectors and the time taken for light to travel this distance:
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Distance between detectors: Given distance = 45 m.
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Calculate time taken by particles to travel between detectors: The speed of the particles is given as 0.97c, where c = speed of light (approximately m/s). Therefore, speed = 0.97 * m/s = m/s.
The time for the particles to reach the second detector is:
= 1.54 imes 10^{-7} ext{ s}.$$ -
Intensity Relation and Half-Life Calculation: The intensity at the second detector is 12.5% of that at the first detector, suggesting a reduction in intensity related to the half-life. Given that intensity diminishes with time, we can deduce that
The first half-life corresponds to a 50% intensity. Since we have 12.5%, we can say: ext{Intensity} = rac{1}{2^n} imes ext{Initial Intensity}, Where n is the number of half-lives. Solving for n when intensity is 12.5% gives us n=3. Therefore, the relationship yields: ext{Half-life} = rac{1.54 imes 10^{-7} ext{ s}}{3} = 5.13 imes 10^{-8} ext{ s}.
Step 3
Identify the proper time in the calculation in Question 04.2.
Answer
The proper time in the calculation is the time measured in the rest frame of the particles. It is defined as the shortest observable time for a particle passing between the detectors when they are at rest relative to each other. In this context, the proper time is the time taken for the particle beam to travel between the two detectors in the reference frame of the particle beam.