Question

The kinetic energy of a moving object is E=12mv2. A 61 kg runner is moving at 10kmh. However, her speedometer is only accurate to within 0.1kmh. What is the potential error in her calculated kinetic energy, as a result of the imprecision in the measurement of her velocity?

Answer 1

`e=3367.2J`

%
`e=1.43`%

Step-by-step explanation:

From the exercise we know two information. The real speed and the experimental measured by the speedometer

`v_(r)=10km/h=2.77m/s`

Since the speedometer is only accurate to within 0.1km/h the experimental speed is

`v_(e)=10km/h-0.1km/h=9.9km/h=2.75m/s`

Knowing that we can calculate Kinetic energy for the real and experimental speed

`E_(r)=(1)/(2)mv^2=(1)/(2)(61000g)(2.77m/s)^2=234023J`

`E_(e)=(1)/(2)mv^2=(1)/(2)(61000g)(2.75m/s)^2=230656J`

Now, the potential error in her calculated kinetic energy is:

`e=E_(r)-E_(e)=(234023-230656)J=3367.2J`

%
`e=(E_(r)-E_(e))/(E_(r))x100=((234023-230656)J)/(234023J)x100=1.43`%