The only force acting on a 2.0 kg canister that is moving in an xy plane has a magnitude of 5.0

step 1 By using a work energy theorem that says work is equal to the changing kinetic energy, changing

The only force acting on a 2.0 kg canister that is moving in...

The only force acting on a 2.0 $\mathrm{kg}$ canister that is moving in an xy plane has a magnitude of 5.0 $\mathrm{N}$ . The canister initially has a velocity of 4.0 $\mathrm{m} / \mathrm{s}$ in the positive $x$ direction and some time later has a velocity of 6.0 $\mathrm{m} / \mathrm{s}$ in the positive $y$ direction. How much work is done on the canister by the 5.0 $\mathrm{N}$ force during this time?

The only force acting on a 2.0 $\mathrm{kg}$ canister that is moving in an
xy plane has a magnitude of 5.0 $\mathrm{N}$ . The canister initially has a velocity of 4.0 $\mathrm{m} / \mathrm{s}$ in the positive $x$ direction and some time later has a
velocity of 6.0 $\mathrm{m} / \mathrm{s}$ in the positive $y$ direction. How much work is
done on the canister by the 5.0 $\mathrm{N}$ force during this time?

Key Concepts

Work

Work is a measure of energy transfer that occurs when a force is applied over a displacement. It is calculated as the dot product of force and displacement, accounting only for the component of the force acting in the direction of the movement. In problems involving changes in motion, calculating work helps determine how the energy of a system is altered by external influences.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, quantified by the expression (1/2)mv². Since kinetic energy depends on the square of the velocity, any change in speed will result in a change in kinetic energy, regardless of the direction of motion. This concept is central to analyzing motions where energy transformations occur.

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. This theorem provides a powerful method for solving dynamics problems, allowing one to bypass detailed force and acceleration analyses and directly relate the work done to the increase or decrease of an object's kinetic energy.

Forces in Two Dimensions

In two-dimensional motion, forces and velocities are vector quantities that have both magnitude and direction. Although the calculation of work involves these vectors, ultimately the work done is a scalar quantity. Understanding vector components is important for resolving forces in multiple directions, but when applying the work-energy theorem, one directly focuses on the overall change in kinetic energy.

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