Chapter 6: Work and Machines 

Section 1: Work

• What is work?

  • To many people, the word work means something they do to earn money.
  • The word work also means exerting a force with your muscles.
  • Work: the energy transferred when a force makes an object move
  • There are two conditions that have to be satisfied for a force to do work on an object. One is that the applied force must make the object move, and the other is that the movement must be in the same direction as the applied force.
  • If you hold a stack of books and walk forward, your arms are exerting a force upward. However, the distance the books move is horizontal. Therefore, your arms are not doing work \n on the books.

• Work and Energy

  • When work is done, a transfer of energy always occurs.
  • If something has energy, it can transfer energy to another object by doing work on that object.
  • When you do work on an object, you increase its energy.
  • Energy is always transferred from the object that is doing the work to the object on which the work is done.
  • By carrying a box up the stairs, you are doing work. You transfer energy to the box.
  • The amount of work done depends on the amount of force exerted and the distance over which the force is applied.
  • Work Equation: work (in joules) = applied force (in newtons) X distance (in meters)
  • The distance you use to calculate the work you did is how far the object moved while the force was being applied.
  • A pitcher exerts a force on the ball to throw it to the catcher. After the ball leaves her hand, the pitcher no longer is exerting any force on the ball. She does work on the ball only while it is in her hand.

• Power: the amount of work done in one second.

  • It is a rate, the rate at which work is done.
  • Power is the rate at which work is done.
  • Power Equation: power (in watts) = work (in joules)/time (in seconds)
  • The SI unit for power is the watt (W).
  • Doing work is a way of transferring energy from one object to another. Just as power is the rate at which work is done, power is also the rate at which energy is transferred.
  • When energy is transferred, the power involved can be calculated by dividing the energy transferred by the time needed for the transfer to occur.
  • Power Equation for Energy Transfer: power (in watts) = energy transferred (in joules)/time (in seconds)

Section 2: Using Machines

• What is a machine?

  • Machine: a device that makes doing work easier.

  • Machines can be simple.

  • Some machines, such as knives, scissors, and doorknobs, are used every day to make doing work easier.

• Making Work Easier

  • Machines can make work easier by increasing the force that can be applied to an object.
  • A second way that machines can make work easier is by increasing the distance over which a force can be applied.
  • Machines also can make work easier by changing the direction of an applied force.
  • A car jack is an example of a machine that increases an applied force.
  • Whether the mover slides the chair up the ramp or lifts it directly into the truck, she will do the same amount

  of work. Doing the work over a longer distance allows her to use less force.

  • The work done in lifting an object depends on the change in height of the object.
  • Some machines change the direction of the force you apply.
  • An ax blade changes the direction of the force from vertical to horizontal.

• The Work Done by Machines

  • A crow bar increases the force you apply and changes its direction.
  • Two forces are involved when a machine is used to do work.
  • Input Force: force that is applied to the machine
  • Output Force: The force applied by the machine
  • Two kinds of work need to be considered when you use a machine: the work done by you on the machine and the work done by the machine.
  • Because energy cannot be created or destroyed, the amount of energy the machine transfers to the object cannot be greater than the amount of energy you transfer to the machine.
  • The input work is the product of the input force and the distance over which the input force is exerted.
  • The output work is the product of the output force and the distance over which that force is exerted.
  • When prying a nail out of a piece of wood with a claw hammer, you exert the input force on the handle of the hammer, and

  the claw exerts the output force.

• Mechanical Advantage: The ratio of the output force to the input force

  • Machines such as the car jack, the ramp, the crow bar, and the claw hammer make work easier by making the output force greater than the input force.
  • Mechanical Advantage Equation: mechanical advantage: output force (in newtons)/input force (in newtons)
  • The mechanical advantage of a machine without friction is called the ideal mechanical advantage, or IMA.

• Efficiency: a measure of how much of the work put into a machine is changed into useful output work by the machine.

  • For real machines, some of the energy put into a machine is always converted to thermal energy by frictional forces.
  • A machine with high efficiency produces less thermal energy from friction, so more of the input work is changed to useful output work.
  • Efficiency Equation: efficiency (%) = output work (in joules)/input work (in joules) X 100%
  • In an ideal machine, there is no friction and the output work equals the input work.
  • In a real machine, friction causes the output work to always be less than the input work.
  • Machines can be made more efficient by reducing friction.

Section 3: Simple Machines

• Types of Simple Machines

  • Simple Machine: a machine that does work with only one movement of the machine.
  • There are six types of simple machines: lever, pulley, wheel and axle, inclined plane, screw, and wedge.
  • The pulley and the wheel and axle are modified levers, and the screw and the wedge are modified inclined planes.

• Lever: a bar that is free to pivot or turn around a fixed point.

  • The fixed point the lever pivots on is called the fulcrum.
  • The input arm of the lever is the distance from the fulcrum to the point where the input force is applied.
  • The output arm is the distance from the fulcrum to the point where the output force is exerted by the lever.
  • If the output arm is longer than the input arm, the law of conservation of energy requires that the output force be less than the input force. If the output arm is shorter than the input arm, then the output force is greater than the input force.
  • For a first-class lever, the fulcrum is located between the input and output forces. The output force is always in the opposite direction to the input force in a first-class lever.
  • The screwdriver is being used as a first-class lever. The fulcrum is the paint can rim.
  • For a second-class lever, the output force is located between the input force and the fulcrum. The output force is exerted between the input force and the fulcrum. For a second-class lever, the output force is always greater than the input force.
  • A wheelbarrow is a second-class lever. The fulcrum is the wheel
  • For a third-class lever, the input force is applied between the output force and the fulcrum.
  • A baseball bat is a third-class lever. The fulcrum here is the batter’s left hand.
  • IMA of a Lever: ideal mechanical advantage = length of input arm (m)/length of output arm (m)

• Pulley: a grooved wheel with a rope, chain, or cable running along the groove.

  • A pulley can change the direction of the input force or increase the output force, depending on whether the pulley is fixed or movable.
  • A system of pulleys can change the direction of the input force and make the output force larger.
  • A fixed pulley changes only the direction of a force. You need to apply an input force of 4 N to lift the 4-N weight.
  • A pulley in which one end of the rope is fixed and the wheel is free to move is called a movable pulley.
  • A movable pulley and a pulley system called a block and tackle reduce the force needed to lift a weight.
  • A system of pulleys consisting of fixed and movable pulleys is called a block and tackle.

• Wheel and Axle: a simple machine consisting of a shaft or axle attached to the center of a larger wheel, so that the wheel and axle rotate together.

  • Doorknobs, screwdrivers, and faucet handles are examples of wheel and axles.
  • Recall that the mechanical advantage of a lever is the length of the input arm divided by the length of the output arm.
  • IMA of a Wheel and Axle: Ideal Mechanical Advantage = radius of wheel(m)/radius of axis (m)
  • A gear is a wheel and axle with the wheel having teeth around its rim.
  • When two gears of different sizes are interlocked, they rotate at different rates.
  • If the input force is applied to the larger gear, the output force exerted by the smaller gear is less than the input force.

• Inclined Plane: a sloping surface, such as a ramp, that reduces the amount of force required to do work.

  • You do the same work by lifting a box straight up or pushing it up an inclined plane. By pushing the box up an inclined plane, however, the input force is exerted over a longer distance compared to lifting the box straight up. As a result, the input force is less than the force needed to lift the box straight upward.
  • IMA: ideal mechanical advantage = length of slope (m)/height of slope (m)

• Screw: an inclined plane wrapped in a spiral around a cylindrical post

  • A screw has an inclined plane that wraps around the post of the screw.
  • You apply the input force by turning the screw. The output force is exerted along the threads of the screw.
  • The IMA of a screw is related to the spacing of the threads
  • The IMA is larger when the threads are closer together. However, when the IMA is larger, more turns of the screw are needed to drive it into a material.

• Wedge: an inclined plane with one or two sloping sides.

  • Like the screw, the wedge is also a simple machine in which the inclined plane moves through an object or material.

• Compound Machine: Two or more simple machines that operate together

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