Question

Calculated the measurement uncertainty for Kinetic Energy when :mass = 1.3[kg] +/- 0.4[kg]velocity= 5.2 [m/s] +/- 0.2 [m/s]KE= 18 [J] +/- ___________________[kg(m/s2 )m]Measurement uncertainty [measurement x sum of relative uncertainties]

Answer 1

`\rm KE\pm \Delta KE = 17.6\pm 6.8\ J.`

Step-by-step explanation:

Given:

• Mass,
  `\rm m\pm\Delta m = 1.3\pm 0.4\ kg.`

• Velocity,
  `\rm v\pm \Delta v = 5.2\pm 0.2\ m/s.`

where,

`\rm \Delta m,\ \Delta v` are the uncertainties in mass and velocity respectively.

The kinetic energy is given by

`\rm KE = \frac 12 mv^2 = \frac 12 * 1.3* 5.2^2=17.576\approx 17.6\ J.`

The uncertainty in kinetic energy is given as:

`\rm (\Delta KE)/(KE)=(\Delta m)/(m)+(2\Delta v)/(v)\\(\Delta KE)/(17.6)=(0.4)/(1.3)+(2* 0.2)/(5.2)\\(\Delta KE)/(17.6)=0.384\\\Rightarrow \Delta KE = 17.6* 0.384 = 6.7854\ J\approx6.8\ J\\\\Thus,\\\\KE\pm \Delta KE = 17.6\pm 6.8\ J.`