Question

An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 kg * m/s. Find the (a) speed and (b) mass of the object.

Answer 1

a) Let's first write the formulas for the momentum and kinetic energy:

$$p=mv,$$ $$KE=\dfrac{1}{2}mv^2.$$

We can rewrite the formula for the kinetic energy as follows:

$$KE=\dfrac{1}{2}mv^2=\dfrac{1}{2}pv.$$

From this formula we can find the speed of the object:

$$v=\dfrac{2KE}{p}=\dfrac{2\cdot 275\ J}{25.0\ \dfrac{kgm}{s}}=22.0\ \dfrac{m}{s}.$$

b) Finally, from the first equation we can find the mass of the object:

$$m=\dfrac{p}{v}=\dfrac{25.0\ \dfrac{kgm}{s}}{22.0\ \dfrac{m}{s}}=1.14\ kg.$$

Answer:

a) $v=22.0\ \dfrac{m}{s}.$

b) $m=1.14\ kg.$