Question

An object of mass 3.4 kg is moving in a straight line with kinetic energy 59.177 J. A force is applied in the direction of its motion for 2.7 seconds, and as a result, its kinetic energy is multiplied by a factor of 1.57. By what factor is its momentum multiplied?

Answer 1

Its momentum is multiplied by a factor of 1.25

Step-by-step explanation:

First, we calculate the initial velocity of the object:

• K = 0.5 * m * v₁²

• 59.177 J = 0.5 * 3.4 kg * v₁²

• v₁ = 5.9 m/s

With that velocity we can calculate the initial momentum of the object:

• p₁ = v₁ * m

• p₁ = 20.06 kg·m/s

Then we calculate the velocity of the object once its kinetic energy has increased:

• (59.177 J) * 1.57 = 0.5 * 3.4 kg * v₂²

• v₂ = 7.4 m/s

And calculate the second momentum of the object:

• p₂ = v₂ * m

• p₂ = 25.16 kg·m/s

Finally we calculate the factor:

• p₂/p₁ = 1.25