Question

The figure shows an object moving from point B to point A and the gravitational potential energy of the object-Earth system at different points along the trajectory. There are no other forces exerted on the object. The magnitude of the force associated with the gravitational field is constant and has a value F. A particle is launched from point B with an initial velocity and reaches point A having gained U0 joules of kinetic energy. A resistive force field is now set up such that it is directed opposite the gravitational field with a force of constant magnitude 12F. A particle is again launched from point B. How much kinetic energy will the particle gain as it moves from point B to point A?

Answer 1

The amount of kinetic energy that will be gained from the particle as it moves from point B to point A is 12U₀.

Since the particle moves through in a projectile path (trajectory). The gravitational potential energy acts on the particle in the downward direction.

A resistive force refers to a force that resists and acts in the direction opposite to the velocity of a body.

$\mathbf{F_r' = 12 F}$

where:

• resistive force $\mathbf{ F_r'}$ = 12 F

Recall that;

• the gravitational potential energy is constant;
• the kinetic energy at point A from B = U₀

∴

When the particle is launched from B to A, the kinetic energy gained by the particle can be computed as:

• U = $\mathbf{f_r'r}$
• U = 12 F × r
• U = 12 U₀  

Learn more about kinetic energy here:

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