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Physics 1D03 - Lecture 22 Energy, Work and Power

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Physics 1D03 - Lecture 22 HOMEWORK QUESTION Please do this question and hand it by Tuesday after the reading week, in class: A 50kg child slides down a 45 o 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 30 o. Draw a pictures of the problem and determine how far on the 2 nd hill the child ends up (not the height).

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Physics 1D03 - Lecture 22 For every conservative force, we can define a potential energy function U so that W AB U U A U B Examples: Gravity (uniform g) : U g = mgy, where y is height Gravity (exact, for two particles, a distance r apart): U g GMm/r, where M and m are the masses Ideal spring: U s = ½ kx 2, where x is the stretch Electrostatic forces (F=kq 1 q 2 /r), where q are the charges Note the negative

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Physics 1D03 - Lecture 22 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 + U g + U s +... Conservative forces only: W U Work-energy theorem: W K So, K U 0; which means that E does not change with time. Conservation of mechanical energy

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

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

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Physics 1D03 - Lecture 22 Example You slide 20m down a frictionless hill with a slope of 30 o 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 ?

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Physics 1D03 - Lecture 22 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/dt And since W=F. s, dW/dt=Fds/dt=F. v, so sometimes it is useful to write: P=F. v

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Physics 1D03 - Lecture 22 Example An elevator motor delivers a constant force of 2x10 5 N over a period of 10s as the elevator moves 20m. What is the power ? P=W/t =Fs/t =(2x10 5 N)(20m)/(10s) =4x10 5 W The same elevator is moving with an average velocity of: The power is:

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