2. By using the instruments from the task 1, you have determined that it takes 3s for a toy car to travel through the distance of 162cm. What are the
relative uncertainties of the distance and time measurements? Which measurements is the least uncertain?
3. Calculate the average speed of the toy car. Decide whether you can use the weakest link rule to determine the relative uncertainty in speed estimation. Determine the range of possible values for the actual speed of the car.
To determine the relative uncertainties of the distance and time measurements, we can use the formula:
Relative uncertainty = (Standard deviation / Mean) * 100
1. Relative uncertainty of the distance measurement:
We will need the standard deviation and mean of the distances measured. Since these values are not provided, let's assume that the distances measured have a standard deviation of δd and a mean of d.
Relative uncertainty of the distance = (δd / d) * 100
2. Relative uncertainty of the time measurement:
We will use the formula provided to calculate the relative uncertainty of time.
Relative uncertainty of the time = (δt / t) * 100
Where δt is the standard deviation of time measurements and t is the mean of time measurements. Since the standard deviation and mean of the time measurements are not provided, we'll assume a standard deviation of δt and a mean of t.
Now, to determine which measurement is the least uncertain, we can compare the relative uncertainties. The measurement with the lower relative uncertainty would be considered less uncertain.
3. To calculate the average speed of the toy car, we use the formula:
Average speed = Distance / Time
Since the distance is given as 162cm and the time is given as 3s, we can substitute these values into the formula to find the average speed.
Average speed = 162cm / 3s
To decide whether we can use the weakest link rule to determine the relative uncertainty in speed estimation, we need to compare the relative uncertainties of the distance and time measurements. If the relative uncertainty of either measurement is significantly greater than the other, then using the weakest link rule is appropriate.
Finally, to determine the range of possible values for the actual speed of the car, we can use the formula:
Range of possible values = Average speed ± (Average speed * (Relative uncertainty/100))
Substitute the average speed and relative uncertainty of speed to calculate the range of possible values.
To determine the relative uncertainties of the distance and time measurements, we first need to calculate the absolute uncertainties for each measurement. The absolute uncertainty for the distance measurement can be determined by considering the smallest division on the instrument used. Let's assume the smallest division on the ruler is 0.1 cm. As the distance measured is 162 cm, the absolute uncertainty would be ±0.05 cm (half of the smallest division).
Similarly, for the time measurement, let's assume the smallest division on the stopwatch is 0.01 s. As the time measured is 3 s, the absolute uncertainty would be ±0.005 s (half of the smallest division).
To calculate the relative uncertainties, we divide the absolute uncertainties by the measured values and multiply by 100. For the distance measurement:
Relative uncertainty of distance = (0.05 cm / 162 cm) * 100 ≈ 0.031%
For the time measurement:
Relative uncertainty of time = (0.005 s / 3 s) * 100 ≈ 0.167%
Comparing the relative uncertainties, we can see that the relative uncertainty of distance is significantly smaller (0.031% compared to 0.167%). Therefore, the distance measurement is the least uncertain.
To calculate the average speed of the toy car, we use the formula:
Average speed = Distance / Time
Given that the distance traveled is 162 cm and the time taken is 3 s, we can substitute these values into the formula:
Average speed = 162 cm / 3 s ≈ 54 cm/s
Now, let's address the use of the weakest link rule to determine the relative uncertainty in speed estimation. The weakest link rule states that the relative uncertainty in a calculated quantity (in this case, speed) is determined by the quantity with the largest relative uncertainty among the constituent measurements (in this case, distance and time).
Since the relative uncertainty of distance is smaller (0.031%) compared to the relative uncertainty of time (0.167%), we cannot apply the weakest link rule. Therefore, the relative uncertainty of speed cannot be determined solely based on the relative uncertainties of distance and time.
To determine the range of possible values for the actual speed of the car, we need to consider the maximum and minimum values that the distance and time measurements could have taken.
For distance, we can use the absolute uncertainty to determine the range of possible values:
Minimum distance = 162 cm - 0.05 cm = 161.95 cm
Maximum distance = 162 cm + 0.05 cm = 162.05 cm
For time, we can use the absolute uncertainty to determine the range of possible values:
Minimum time = 3 s - 0.005 s = 2.995 s
Maximum time = 3 s + 0.005 s = 3.005 s
Now, we can calculate the range of possible average speed values using these extremes:
Minimum average speed = 161.95 cm / 3.005 s ≈ 53.91 cm/s
Maximum average speed = 162.05 cm / 2.995 s ≈ 54.14 cm/s
Therefore, the range of possible values for the actual speed of the car is approximately between 53.91 cm/s and 54.14 cm/s.