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Figure 10-3 If a force is applied to a car at an angle, the net force doing the work is the component that acts in the direction of the displacement
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Section 101 Energy and Work
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The work you do when you exert a force on an object, at an angle to the direction of motion, is equal to the component of the force in the direction of the displacement, multiplied by the distance moved The magnitude of the component force acting in the direction of displacement is found by multiplying the magnitude of force, F, by the cosine of the angle between F and the direction of the displacement: Fx F cos Thus, the work done is represented by the following equation Work (Angle Between Force and Displacement) W Fd cos
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Work is equal to the product of force and displacement, times the cosine of the angle between the force and the direction of the displacement
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Other agents exert forces on the pushed car as well Which of these agents do work Earth s gravity acts downward, the ground exerts a normal force upward, and friction exerts a horizontal force opposite the direction of motion The upward and downward forces are perpendicular to the direction of motion and do no work For these forces, 90 , which makes cos 0, and thus, W 0 The work done by friction acts in the direction opposite that of motion at an angle of 180 Because cos 180 1, the work done by friction is negative Negative work done by a force exerted by something in the external world reduces the kinetic energy of the system If the person in Figure 10-3a were to stop pushing, the car would quickly stop moving its energy of motion would be reduced Positive work done by a force increases the energy, while negative work decreases it Use the problemsolving strategies below when you solve problems related to work
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When solving work-related problems, use the following strategies 1 Sketch the system and show the force that is doing the work 2 Draw the force and displacement vectors of the system 3 Find the angle, , between each force and displacement 4 Calculate the work done by each force using W Fd cos 5 Calculate the net work done Check the sign of the work using the direction of energy transfer If the energy of the system has increased, the work done by that force is positive If the energy has decreased, then the work done by that force is negative
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10 Energy, Work, and Simple Machines
Work and Energy A 105-g hockey puck is sliding across the ice A player exerts a constant 450-N force over a distance of 0150 m How much work does the player do on the puck What is the change in the puck s energy
Analyze and Sketch the Problem
Sketch the situation showing initial conditions Establish a coordinate system with x to the right Draw a vector diagram Known:
m F d 105 g 450 N 0150 m
x F d
Unknown:
W KE
Solve for the Unknown
Use the equation for work when a constant force is exerted in the same direction as the object s displacement Math Handbook W Fd Operations with (450 N)(0150 m) Substitute F 450 N, d 0150 m Significant Digits 0675 N m pages 835 836 0675 J 1J 1Nm Use the work-energy theorem to determine the change in energy of the system W KE KE 0675 J Substitute W 0675 J
Evaluate the Answer
Are the units correct Work is measured in joules Does the sign make sense The player (external world) does work on the puck (the system) So the sign of work should be positive
1 Refer to Example Problem 1 to solve the following problem a If the hockey player exerted twice as much force, 900 N, on the puck, how would the puck s change in kinetic energy be affected b If the player exerted a 900 N-force, but the stick was in contact with the puck for only half the distance, 0075 m, what would be the change in kinetic energy 2 Together, two students exert a force of 825 N in pushing a car a distance of 35 m a How much work do the students do on the car b If the force was doubled, how much work would they do pushing the car the same distance 3 A rock climber wears a 75-kg backpack while scaling a cliff After 300 min, the climber is 82 m above the starting point a How much work does the climber do on the backpack b If the climber weighs 645 N, how much work does she do lifting herself and the backpack c What is the average power developed by the climber
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