Pushing a Cat. Your cat "Ms." (mass 7.00 kg) is trying to...

Pushing a Cat. Your cat "Ms." (mass 7.00 kg) is trying to make it to the top of a frictionless ramp 2.00 $\mathrm{m}$ long and inclined upward at $30.0^{\circ}$ above the horizontal. Since the poor cat can't get any traction on the ramp, you push her up the entire length of the ramp by exerting a constant $100-\mathrm{N}$ force parallel to the ramp. If Ms. takes a running start so that she is moving at 2.40 $\mathrm{m} / \mathrm{s}$ at the bottom of the ramp, what is her speed when she reaches the top of the incline? Use the work-energy theorem.

Pushing a Cat. Your cat "Ms." (mass 7.00 kg) is trying to make it to the top of a frictionless ramp 2.00 $\mathrm{m}$ long and inclined upward at $30.0^{\circ}$ above the horizontal. Since the poor cat
can't get any traction on the ramp, you push her up the entire length of the ramp by exerting a constant $100-\mathrm{N}$ force parallel to the ramp. If Ms. takes a running start so that she is moving at
2.40 $\mathrm{m} / \mathrm{s}$ at the bottom of the ramp, what is her speed when she reaches the top of the incline? Use the work-energy theorem.

Key Concepts

Work-Energy Theorem

This principle states that the work done by all forces on an object is equal to the change in its kinetic energy. It provides a framework for understanding how different forms of energy, such as kinetic and potential energies, are transformed when forces do work on the object.

Kinetic Energy

This is the energy an object possesses due to its motion and is calculated using the formula ½mv². Changes in kinetic energy are a key focus when applying the work-energy theorem, as they are directly related to the work performed on the object.

Gravitational Potential Energy

This form of energy is associated with an object's position within a gravitational field and is given by the product mgh, where m is the mass, g is the gravitational acceleration, and h is the height. It plays a crucial role in problems where elevation changes are involved, such as motion along an inclined plane.

Work Done by a Constant Force

This concept involves calculating the work as the product of a constant force and the displacement in the direction of the force. It is essential in analyzing situations where an external force contributes to the overall change in mechanical energy of a system.

Inclined Plane

An inclined plane is a flat surface set at an angle to the horizontal, which is commonly used to study energy transformations in the presence of gravitational forces. It requires breaking forces into components, particularly when calculating the work done and the corresponding changes in gravitational potential energy.

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