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

Kinetic energy = momentum^2 / 2 x mass
Mass = (momentum^2/ Kinetic energy) / 2

Mass =  (25^2 / 275) / 2
Mass = 1.136 kg.

momentum = mass x velocity

velocity = mass / momentum
velocity = 1.136 / 25
velocity = 0.04544 m/s

Answer 2

Answer: The correct answers are 482.4 m/s and 21.96 kg.

Explanation:

The expression for the kinetic energy in terms of momentum of an object is as follows;

$KE=\frac{p^{2} }{2m}$

Here, KE is the kinetic energy, p is the momentum and m is the mass of the object.

It is given in the problem that an object has a kinetic energy of 275 j and a momentum of magnitude 25.0 kg · m/s.

Calculate the mass of the object.

$KE=\frac{p^{2} }{2m}$

Put p=25.0 kg · m/s and KE= 275 J.

$m=\frac{25^{2} }{2(275)}$

$m=1.14 kg$

Calculate the speed of the object.

$KE=\frac{1}{2} mv^{2}$

Put m= 1.14 kg and KE= 275 J.

$v=\sqrt{\frac{2(275)}{1.14} }$

v=21.96 m/s

Therefore, the speed of the object is 21.96 m/s and the mass of the object is 1.14 kg.