You and your bicycle have combined mass 80.0 kg . When you reach the bridge, you are traveling a

step 1 Question number 73, the total work done in part A is equal to W equal to the change in kinetic e

You and your bicycle have combined mass 80.0 kg . When you...

You and your bicycle have combined mass 80.0 $\mathrm{kg} .$ When you reach the bridge, you are traveling along the road at 5.00 $\mathrm{m} / \mathrm{s}($ Fig. $\mathrm{P} 6.78)$ . At the top of the bridge, you have climbed a vertical distance of 5.20 $\mathrm{m}$ and have slowed to 1.50 $\mathrm{m} / \mathrm{s} .$ You can ignore work done by friction and any inefficiency in the bike or your legs. (a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? (b) How much work have you done with the force you apply to the pedals?

You and your bicycle have combined mass 80.0 $\mathrm{kg} .$ When you reach the bridge, you are traveling along the road at 5.00 $\mathrm{m} / \mathrm{s}($ Fig. $\mathrm{P} 6.78)$ . At the top of the bridge, you have climbed a vertical distance of 5.20 $\mathrm{m}$ and have slowed to 1.50 $\mathrm{m} / \mathrm{s} .$ You can ignore work done by friction and any inefficiency in the bike or
your legs. (a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? (b) How much work have you done with the force you apply to the pedals?

Key Concepts

Work–Energy Theorem

This theorem states that the net work done on an object is equal to the change in its kinetic energy. In problems like this, it is used to relate the work acting on the system to the modification of the object's speed, taking the difference between the initial and final kinetic energies.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. In the context of this problem, the change in gravitational potential energy is calculated based on the vertical displacement of the object, reflecting the energy required to elevate the object against gravity.

Kinetic Energy

Kinetic energy is the energy of motion and is given by one?half the product of mass and the square of the velocity. It is a key factor in determining the energy state of an object at any point and is directly involved in the work–energy calculations when an object accelerates or decelerates.

Energy Conservation

The principle of energy conservation asserts that in an isolated system, energy can neither be created nor destroyed; it only transforms from one form to another. In this scenario, ignoring friction, the work done by one force, such as the applied force at the pedals, is manifested as changes in both kinetic and potential energy.

Applied Work versus Net Work

This concept differentiates between the total work done on an object (net work) and the work provided by a specific force. In system analysis, net work considers the sum of all forces acting (including conservative forces like gravity), while the work applied (such as by the rider at the pedals) is usually calculated based on the energy input necessary to achieve the observed changes in the system.

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