To calculate the work done by a force on an object, you need to use the formula:
Work = Force × Distance × cos(θ)
However, in this case, we are not given the distance or the angle (θ). Therefore, we need to find an alternative method to calculate the work done using the given information.
The work done by a force can also be calculated using the change in kinetic energy. The change in kinetic energy (ΔKE) is given by:
ΔKE = KEf - KEi
Where: KEf = Final kinetic energy KEi = Initial kinetic energy
The initial kinetic energy is given by:
KEi = 0.5 × mass × initial velocity²
And the final kinetic energy is given by:
KEf = 0.5 × mass × final velocity²
Let's calculate the initial and final kinetic energies:
Initial kinetic energy: KEi = 0.5 × 4 kg × (3 m/s)² = 0.5 × 4 kg × 9 m²/s² = 18 J
Final kinetic energy: KEf = 0.5 × 4 kg × (5 m/s)² = 0.5 × 4 kg × 25 m²/s² = 50 J
Now we can calculate the change in kinetic energy:
ΔKE = KEf - KEi = 50 J - 18 J = 32 J
The work done by the force is equal to the change in kinetic energy:
Work = ΔKE = 32 J
Therefore, the work done by the force on the object is 32 joules (J).