Phys 201 1nd Edition Lecture 15 Outline of Last Lecture I. Non-conservative work and energy with a spring.Outline of Current Lecture II. External vs. Internal WorkIII. PowerA. Power in terms of SpeedIV. Air ResistanceV. Linear MomentumA. ImpulseCurrent LectureExternal vs. Internal Work:Remember that work can be positive or negative. If work is positive, then energy is going into a system. Ifwork is negative, then energy is going out of a system. Work done by an internal conservative force does not leave the systemWext=ΔEExternal work can change the total energy of a system. For example, if a ball is thrown straight up in the air and the forces working on it are gravity and air resistance, then compared to the time it takes for the ball to go up, it takes more time for the ball to come down. This is because, due to air friction, the ball is continuously losing kinetic energy.Power:Power describes the speed at which work is done. Essentially, power is calculated as a change in energy over a change in time. The equation for this is;Power=ΔW/ΔtBecause power is energy over time, the unit for power is J/s, which are also called Watts. If you think about a machine or appliance with a certain wattage, this same equation can be used to find out how much energy the appliance uses in a certain amount of time, just convert the equation to solve for work. These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Example: An electric motor lifts a 50kg mass a distance of 6m. The motor can put out 1000 Watts of power. How long will it take the motor to move the object?P=ΔW/ΔTP=FΔX/Δt  Δt=FX/P  Δt=mgX/P = (50)(9.81)(6)/1000=2.94sPower in Terms of Speed: If you consider the ball example from above, the loss of kinetic energy as the ball is falling causes the speed of the ball to decrease. Because work is a measure of kinetic energy, this means that the speed of an object can also affect the power of that object. If you think about the fact that work is force times a change in position, and speed is a change is position over a change in time, then power can also be calculated by multiplying force times speed. We can describe this association equationally as; P=ΔW/ΔT  P=FΔX/Δt  P=FVIf you apply a force to something at a certain speed, then there is a certain amount of power required. However, in a lot of cases there is a limit of the amount of power that can be had. Humans, for example, are only physically capable of producing so much power. Therefore, if a person continues to increase the force they are applying to something, they will have to adjust their speed in order to stay within the parameters of their available power. For example, think about riding a bike up a hill. If the hill is really steep, or if the hill is grass instead of concrete and therefore has more friction, then it is much harder to move up the hill, and you will have to apply more force to keep moving. The harder it is to move up the hill, the slower you move up the hill. Air resistance: Consider the ball example again. We mentioned that the forces working on the ball were gravity and air resistance, and that the air resistance affected the kinetic energy, and therefore the speed, of the ball. Up until now we have ignored the effects of air resistance on a falling object. The force of air resistance isdirectly proportional to the speed at which an object is moving. The equation for the force of air resistance is;F=AV2For this equation, A is a constant. The value of A differs based on the shape of the object. Because force can be calculated as power over velocity, we can also calculate the power of air resistance by converting the equation into the following;F=AV2  P/V=AV2  P=AV3Linear momentum:Remember Newton’s first law: An object at rest will remain at rest, while an object in motion will remain in motion in the same direction until acted upon by an unbalanced force. In this case, the change in motion caused by a force is known as momentum.The momentum of a force can be calculated by multiplying mass by velocity, where momentum and velocity are vectors, meaning that they have direction. Momentum is represented by ρ. ρ=mVForce is calculated by multiplying mass and acceleration (F=ma). Acceleration is defined as a change in velocity over a change in time (a=ΔV/Δt). If we put these equations together, we get the following;F=ma  F=m(ΔV/Δt)  F= Δ(mV)/Δt Because momentum is mass times velocity, if we want to consider the magnitude of a force in terms of its momentum, then we can convert this equation to;F= Δ(mV)/Δt  F=Δρ/ΔtThis means that we can define force is a change in momentum over a change in time. This applies directly to Newton’s second law of motion. We know that Favg=Δρ/Δt. This means that to solve for momentum in terms of force, we can rearrange this equation to be Δρ=FavgΔt. In this case, FΔt is the change in momentum, which is referred to as “impulse”. The impulse helps relate actual force to average force. The most common example of an impulse is in the case of a collision. When an object collides with another, an opposite force is experienced for a certain amount of time, and it causes the momentum of the object to change. This force in this amount of time experienced is an impulse, and it is equal to the momentum of the object and is responsible for causing a change in that momentum.Example: A 70kg soccer player kicks a .5kg ball, giving it a speed of 14m/s. The contact time of the foot on the ball is .1s. a) What is the force on the ball? b) What is the force on the foot?a) Kicking the ball changes the balls momentum. Therefore, we can use the momentum equation to solve for the force. FΔt=Δρ Δρ=ρf-ρi =mVf - mVi = (14)(.5)-0 =7FΔt=Δρ  FΔt=7kgm/s  F=7/Δt =7/.1= 70Nb) There is no need to calculate the force on the foot. Consider Newton’s third law (For every action there is an equal and opposite reaction). This means that the force on the foot will be the same as the force on the foot, just in the opposite