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Energy, Work and Power

Energy, Work and Power. HOMEWORK QUESTION. Please do this question and hand it by Tuesday after the reading week, in class:

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Energy, Work and Power

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  1. Energy, Work and Power Physics 1D03 - Lecture 22

  2. HOMEWORK QUESTION Please do this question and hand it by Tuesday after the reading week, in class: A 50kg child slides down a 45o frictionless hill for 60m, starting with an initial velocity of 2m/s. The child then slides for 10m over a flat surface that has a coefficient of kinetic friction of 0.15, and finally back up another frictionless hill with a slope of 30o. Draw a pictures of the problem and determine how far on the 2nd hill the child ends up (not the height). Physics 1D03 - Lecture 22

  3. For every conservative force, we can define a potential energy function U so that WAB=-DU = UA-UB Note the negative Examples: Gravity (uniform g) : Ug = mgy, where y is height Gravity (exact, for two particles, a distance r apart): Ug=- GMm/r, where M and m are the masses Ideal spring: Us = ½ kx2,where x is the stretch Electrostatic forces (F=kq1q2/r), where q are the charges Physics 1D03 - Lecture 22

  4. Conservation of mechanical energy If only conservative forces do work, potential energy is converted into kinetic energy or vice versa, leaving the total constant. Define the mechanical energy E as the sum of kinetic and potential energy: E K + U = K + Ug + Us +... Conservative forces only: W = -DU Work-energy theorem: W = DK So, DK+DU = 0; which means that E does not change with time. Physics 1D03 - Lecture 22

  5. Example: Pendulum L • The pendulum is released from rest with the string horizontal. • Find the speed at the lowest point (in terms of the length L of the string). vf Physics 1D03 - Lecture 22

  6. Example: Pendulum θ • The pendulum is released from rest at an angle θ to the vertical. • Find the speed at the lowest point (in terms of the length L of the string). vf Physics 1D03 - Lecture 22

  7. Example You slide 20m down a frictionless hill with a slope of 30o starting from rest. At the bottom you collide and stick to another person (at rest) that has 90% of your mass.a) Determine the final velocity of the system.b) How would the calculation and final velocity change if the slope had a coefficient of kinetic friction of 0.1 ? Physics 1D03 - Lecture 22

  8. Power The time rate of doing work is called power.If an external force is applied to an object, and if work is done by this force in a time interval Δt, the average power is defined as: P=W/Δt (unit: J/s = Watt, W)For instantaneous power, we would use the derivative:P=dW/dtAnd since W=F.s, dW/dt=Fds/dt=F.v, so sometimes it is useful to write:P=F . v Physics 1D03 - Lecture 22

  9. Example An elevator motor delivers a constant force of 2x105N over a period of 10s as the elevator moves 20m. What is the power ?P=W/t =Fs/t =(2x105N)(20m)/(10s) =4x105 W The same elevator is moving with an average velocity of: The power is: Physics 1D03 - Lecture 22

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