6.Kinetic energy and work

An angle of 300o downward from the horizontal the

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Unformatted text preview: e pull F2 of spy 002 is 10.0 N directed at 40.0 o above the horizontal. The magnitudes and directions of these forces do not change as the save moves, and the floor and safe make frictionless contact. Work and kinetic energy theorem: The change in kinetic energy of an object equals the work done on the object. ∆K = K f − K i = W Change in the kinetic energy of a particle = Net work done on the particle 1. = kinetic energy before the net work is done + During the displacement, whit is the work done by gravitational force and the normal force? 3. The net work done What is the work done by F1 and F2 during the displacement d. 2. K f = Ki + W kinetic energy after the net work is done 8 r F2 r F1 The safe is initially stationary. What is the speed at the end of the 8.5m displacement. The Department of Physics, CUHK The Department of Physics, CUHK 9 §6. Work done by the gravitational force If we use mg as the gravitational force, then the work done by the gravitational force is: Sample problem 7-5 An initially stationary 15.0kg crate of cheese wheels is pulled via a cable, a distance d=5.70 m up a frictionless ramp to a height of 2.5m, where it is stops. r v 1. r Fg = − mgd How much work is done on the crate by the gravitational force? 2. Kf W g = mgd cos θ W g = mgd cos 180 o 10 How much work is done by the force T from the cable during the lift? r d r v0 r Fg Ki m r T frictionless m The Department of Physics, CUHK h θ The Department of Physics, CUHK 11 12 2 §7. Work done by a spring force We want to examine the work done by a particular type of variable force – namely, a spring force . spring Hooke Robert Hooke Born: 18-Jul-1635 Birthplace: Freshwater, Isle of Wight, England Died: 3-Mar-1703 Hooke’s law: Fx = − kx k is the spring constant The Department of Physics, CUHK The Department of Physics, CUHK 13 Work done by a spring force Work done by a spring force W s = ∑ − Fx ∆ x In the limit as ∆ x x0 x0 Ws = Ws = x1 x 0 x1 ∆ x ∆ W s = − Fx ∆ x 14 ∫ xf xi xf ∫x Now suppose that we displace the block along x axis while continuing to apply a force Fa to it. The change in the kinetic energy of the block is →0 − Fx dx ∆K = K f − K i = Wa + Ws So if the change of kinetic energy is zero, − kxdx i W a = −W s W s = 1 kx i2 − 1 kx 2 f 2 2 If Note: Therefore, if a block is attached to a spring is stationary before and after a displacement, the work done by the applied force displacing is the negative of the work done on it by the spring force. xi = 0 W s = − 1 kx 2 2 The Department of Physics, CUHK The Department of Physics, CUHK 15 §8. Work done by a general variable force Sample problem 7-8 In the right figure, a cumin of mass m=0.40kg slides across a horizontal frictionless counter with speed v=0.50m/s. It then runs into and compresses a spring of spring constant k=750N/m. When the canister is momentarily stopped by the spring, by what distance d is the spring is compressed? 16 r v k F ( x) Let’s consider a general va...
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This document was uploaded on 09/16/2013.

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