Question

1. suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. what is the uncertainty in your mass (in kilograms)?
2. a good - quality measuring tape can be off by 0.50 cm over a distance of 20 m. what is its percent uncertainty?
3. (a) a car speedometer has a 5.0% uncertainty. what is the range of possible speeds when it reads 90 km/h? (b) convert this range to miles per hour. (1 km = 0.6214 mi)
4. an infant’s pulse rate is measured to be 130 ± 5 beats/min. what is the percent uncertainty in this measurement?

Explanation:

11.

Step1: Identify the formula

Percent - uncertainty formula is $\text{Percent Uncertainty}=\frac{\Delta x}{x}\times100\%$, where $\Delta x$ is the uncertainty and $x$ is the measured value. We want to find $\Delta x$, and we know that $\text{Percent Uncertainty} = 3\%=0.03$ and $x = 65$ kg. Rearranging the formula gives $\Delta x=\text{Percent Uncertainty}\times x$.

Step2: Calculate the uncertainty

$\Delta x=0.03\times65$ kg = 1.95 kg

Step1: Identify the values

The measured value $x = 20$ m = 2000 cm and the uncertainty $\Delta x=0.50$ cm.

Step2: Use the percent - uncertainty formula

$\text{Percent Uncertainty}=\frac{\Delta x}{x}\times100\%=\frac{0.50}{2000}\times100\%$

Step3: Calculate the result

$\frac{0.50\times100}{2000}= 0.025\%$

Step1: Identify the formula for uncertainty

Percent - uncertainty formula is $\text{Percent Uncertainty}=\frac{\Delta v}{v}\times100\%$, where $\Delta v$ is the uncertainty in speed and $v$ is the measured speed. Given $\text{Percent Uncertainty}=5.0\% = 0.05$ and $v = 90$ km/h. Rearranging for $\Delta v$ gives $\Delta v=\text{Percent Uncertainty}\times v$.

Step2: Calculate the uncertainty

$\Delta v=0.05\times90$ km/h = 4.5 km/h

Step3: Find the range of speeds

The lower - bound speed $v_{min}=v-\Delta v=90 - 4.5=85.5$ km/h and the upper - bound speed $v_{max}=v + \Delta v=90+4.5 = 94.5$ km/h

Answer:

1.95 kg

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