Energy

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This caused the system to gain the ability Observation: In each of these scenarios, the external force exerted on the system was in the same direction as the system’s displacement. This caused the system to gain the ability to do something new: The block at higher elevation above Earth could break the chalk. The fast-moving cart could break the chalk. The stretched slingshot could break the chalk. The box and the floor it was pulled across became warmer.

The faster the cart is moving, the more K it has. In scenario 1, the hand did positive work that increased the kinetic energy (K) of the cart, giving it the additional energy needed to break the chalk. The faster the cart is moving, the more K it has.

In scenario 2, the hand did positive work that increased the gravitational potential energy (Ug) of the Earth-block system, giving them the additional energy needed to break the chalk. The higher up the block is, the greater the Ug of the Earth-block system.

The more a spring is stretched (or compressed), the more Us it has. In scenario 3, the hand did positive work that increased the elastic potential energy (Us) of the slingshot, giving it the additional energy needed to break the chalk. The more a spring is stretched (or compressed), the more Us it has.

In scenario 4, the hand did positive work that increased the internal energy (Uint) of the box/floor system, warming them up and causing tiny scratches and deformations. You will learn later that internal energy is based on the motion and interaction of microscopic particles that make up a system.

Work – The transfer of energy to or from a system by an external force over a displacement. In each of these scenarios, positive work was done on the system by the external force of the person’s hand (part of the the environment). This positive work caused the energy of the system to increase.

Positive work occurs when the total energy of the system increases. Negative work occurs when the total energy of the system decresases. Zero work occurs when the total energy of the system remains unchanged.

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This caused the system to lose the ability to break the chalk. Observation: In these scenarios, the external force exerted on the system was in the opposite direction as the system’s displacement. This caused the system to lose the ability to break the chalk. The block at lower elevation (but still zero speed) could not break the chalk. The stationary cart could not break the chalk.

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This caused no change in the system’s energy. Observation: In this scenario, the external force exerted on the system was perpendicular to the system’s displacement. This caused no change in the system’s energy. The block at the same elevation and same speed has the same amount of energy. The normal force does not affect the cart’s ability to break the chalk.

+ (max) + - - max

Figure 6.1

1 Joule = 1 Newton * 1 meter = 1 N*m 𝑊 1𝑜𝑛2 = 𝐹 1𝑜𝑛2 ∙𝑑∙𝑐𝑜𝑠(𝜃) Units: Joules (J) Named in honor of James Joule (1818-1889), who greatly improved our understanding of work-energy relationships. 1 Joule = 1 Newton * 1 meter = 1 N*m

Work and energy are scalar quantities. Although work depends on the relative direction of the force and displacement vectors, it is not itself a vector quantity. Positive work = Energy is transferred into the system. Negative work = Energy is transferred out of the system. With work and energy, positive/negative have nothing to do with direction.

Two friends are cycling up a hill inclined at 8° Two friends are cycling up a hill inclined at 8°. The cyclist on the left helps his friend by exerting a 50-N force on his friend parallel to the hill. During this time, the bicycles travel a distance of 100 m. Determine the work done by the left cyclist on the right cyclist. Unnumbered Figure Page 189

You pull a box 20 m up a 10° ramp You pull a box 20 m up a 10° ramp. The rope is oriented 20° above the horizontal, as shown. The force that the rope exerts on the box is 100 N. How much work does the rope do on the box? Unnumbered Figure Page 190

A car coasts down a hill with three forces acting on it, as shown below. Specify if the work done by each force is positive, negative, or zero. Support your answers using force and displacement vectors, as well the the concept of work as a transfer of energy.

You want to load a box into the back of a truck You want to load a box into the back of a truck. One way is to lift it straight upward at constant speed through a height h, as shown. Alternatively, you can slide the box up a frictionless loading ramp at a constant speed over a distance L. The ramp is raised at an angle φ above the horizontal. Compare the work done on the box-Earth system in each case. Show all calculations to support your answer.