Efficiency Efficiency Real machines are not frictionless Some

Efficiency • Real machines are not frictionless. Some of the input energy is dissipated

A machine is 75 percent efficient. If 200 joules of work are put into

The work output is 300 joules for a machine that is 50 percent efficient.

A person uses a 75 -newton force to push a 51 -kilogram car up

Mechanical Advantage • Because the purpose of a simple machine is to change the

A machine uses an input force of 200 newtons to produce an output force

A machine is required to produce an output force of 600 newtons. If the

A person lifts a 950 N box by pushing it up an incline. If

What is the mechanical advantage of a lever that allows Jorge to lift a

A construction worker uses a board and log as a lever to lift a

A child’s toy rake is held so that its output arm is 0. 75

A lever used to lift a heavy box has an input arm of 4

Mechanical advantage of a ramp The input work is the input force multiplied by

A 5 -meter ramp lifts objects to a height of 0. 75 meters. What

A ramp with a mechanical advantage of 6 is used to move a 36

A bicycle traveled a distance of 100 meters. The diameter of the wheel of

A particle is moving around in a circle of radius R = 1. 5

During the spin cycle of a washing machine, the clothes stick to the outer

The maximum speed with which a 945 -kg car makes a 180 -degree turn

A pilot is flying a small plane at 56. 6 m/s in a circular

A 4. 0 kg ball is attached to 0. 7 meter string and spun

Find the distance between a 0. 300 kg billiard ball and a 0. 400

Find the gravitational force a 66. 5 kg person would experience while standing on

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Efficiency

Efficiency • Real machines are not frictionless. Some of the input energy is dissipated as sound or heat. • The efficiency of a machine is the ratio of useful work output to work input. – The efficiency of an ideal (frictionless) machine is 1, or 100 percent. – The efficiency of real machines is always less than 1.

A machine is 75 percent efficient. If 200 joules of work are put into the machine, how much work output does it produce?

The work output is 300 joules for a machine that is 50 percent efficient. What is the work input?

A person uses a 75 -newton force to push a 51 -kilogram car up a ramp. The ramp is 10 meters long and rises one meter. Calculate the efficiency.

Simple Machines & Mechanical Advantage

Mechanical Advantage • Because the purpose of a simple machine is to change the direction or magnitude of an input force, a useful way of characterizing a simple machine is to compare the output and input force. • This ratio is called mechanical advantage. • If friction is disregarded, mechanical advantage can also be expressed in terms of input and output distance.

A machine uses an input force of 200 newtons to produce an output force of 800 newtons. What is the mechanical advantage of this machine?

A machine uses an input force of 200 newtons to produce an output force of 800 newtons. What is the mechanical advantage of this machine? Fout = 800 N Fin = 200 N MA = 800 N/200 N = 4

A machine is required to produce an output force of 600 newtons. If the machine has a mechanical advantage of 6, what input force must be applied to the machine?

A machine is required to produce an output force of 600 newtons. If the machine has a mechanical advantage of 6, what input force must be applied to the machine? Fout = 600 N MA = 6 Fin = Fout/MA = 600 N/6 = 100 N

A person lifts a 950 N box by pushing it up an incline. If the person exerts a force of 350 N along the incline, what is the mechanical advantage of the incline?

What is the mechanical advantage of a lever that allows Jorge to lift a 24 -newton box with a force of 4 newtons?

A construction worker uses a board and log as a lever to lift a heavy rock. If the input arm is 3 meters long and the output arm is 0. 75 meters long, what is the mechanical advantage of the lever?

A construction worker uses a board and log as a lever to lift a heavy rock. If the input arm is 3 meters long and the output arm is 0. 75 meters long, what is the mechanical advantage of the lever? Lin = 3 m Lout = 0. 75 m MA = 3 m/0. 75 m = 4

A child’s toy rake is held so that its output arm is 0. 75 meters. If the mechanical advantage is 0. 33, what is the input arm length?

A lever used to lift a heavy box has an input arm of 4 meters and an output arm of 0. 8 meters. What is the mechanical advantage of the lever?

Mechanical advantage of a ramp The input work is the input force multiplied by the length of the ramp (10 meters). If you set the input work equal to the output work, you quickly find that the input force is 50 newtons (Fd = F × 10 m = 500 J). The input force is one-tenth of the output force. For a frictionless ramp, the mechanical advantage is the length of the ramp divided by the height.

A 5 -meter ramp lifts objects to a height of 0. 75 meters. What is the mechanical advantage of the ramp?

A ramp with a mechanical advantage of 6 is used to move a 36 -newton load. What input force is needed to push the load up the ramp?

Circular Motion

A bicycle traveled a distance of 100 meters. The diameter of the wheel of this bicycle is 40 cm. Find the number of rotations of the wheel.

A bicycle traveled a distance of 100 meters. The diameter of the wheel of this bicycle is 40 cm. Find the number of rotations of the wheel. 40 cm = 0. 4 m (2*3. 14*0. 2 m) = 1. 256 m 100 m / 1. 256 m = 79. 6 rotations

A particle is moving around in a circle of radius R = 1. 5 m with a constant speed of 2 m/s. What is the angular velocity of the particle?

A particle is moving around in a circle of radius R = 1. 5 m with a constant speed of 2 m/s. What is the angular velocity of the particle? C = (2*3. 14*1. 5) = 9. 42 m 2 m/s = 120 m per min 120/9. 42 = 17. 73 rpm

During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm. Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel.

Centripetal Force

The maximum speed with which a 945 -kg car makes a 180 -degree turn is 10. 0 m/s. The radius of the circle through which the car is turning is 25. 0 m. Determine the force of friction acting upon the car.

A pilot is flying a small plane at 56. 6 m/s in a circular path with a radius of 188. 5 m. The centripetal force needed to maintain the plane’s circular motion is 1. 89 x 10^4 N. What is the plane’s mass?

A 4. 0 kg ball is attached to 0. 7 meter string and spun at 2. 0 meters/sec. What is the centripetal force?

A 4. 0 kg ball is attached to 0. 7 meter string and spun at 2. 0 meters/sec. What is the centripetal force? 22. 85 N

Gravitational Force

Find the distance between a 0. 300 kg billiard ball and a 0. 400 kg billiard ball if the magnitude of the gravitational force between them is 8. 92 x 10 -11 N.

Find the distance between a 0. 300 kg billiard ball and a 0. 400 kg billiard ball if the magnitude of the gravitational force between them is 8. 92 x 10 -11 N. r= 0. 30 m

Find the gravitational force a 66. 5 kg person would experience while standing on the surface of Mars has a mass of 6. 42 x 10^23 kg and a radius of 3. 40 x 10^6 m.