If the mass of an object is doubled while maintaining the same energy, what happens to its travel distance?

When the mass of an object is doubled while maintaining the same energy, its travel distance is impacted due to the relationship between energy, mass, and velocity. The kinetic energy of an object is given by the formula:

[ KE = \frac{1}{2} mv^2 ]

where ( KE ) is kinetic energy, ( m ) is mass, and ( v ) is velocity. If we keep the energy constant while doubling the mass, we can analyze the equation.

Let's say the initial mass is ( m ) and it has an initial velocity ( v ). The initial kinetic energy can be expressed as:

[ KE = \frac{1}{2} mv^2 ]

If we double the mass to ( 2m ) and keep the kinetic energy the same, we set up the equation for the new scenario:

[ KE = \frac{1}{2} (2m)v'^2 = \frac{1}{2} mv^2 ]

Here, ( v' ) is the new velocity after the mass is doubled. Rearranging gives us:

[ mv^2 = (2m)v'^2 ]

Dividing both sides by ( m ) (assuming (