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A) Inclined planes are simple machines that reduce the amount of force required to lift an object by increasing the distance over which the force is applied. C) Inclined planes allow objects to be moved from a lower to a higher position with less effort compared to lifting the object vertically. E) Inclined planes can be found in everyday objects such as ramps, stairs, and slides.

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A wheel has a radius of 4.3 m How far path length does a point on the circumference travel if the wheel is rotated through angles of 30 30 rad and 30 rev respectively?

The diameter (i.e. the length of the outside) of the wheel is 4.3 meters times Pi (3.14) or abut 13.5 meters.Circumference = 4.3 m x Pi = 4.3 x 3.14 = 13.5mFor a 30 degree rotation, the wagon will have moved forward a fraction of the wheel's circumference that is equal to the percentage of the wheel thatis represented by 30degrees. Since the circumference is represented by 360 dgrees, this percetange is 30/360.Distance moved = (percentage of circumference represented by 30 degrees)x(circumference)= (30 degrees/360 degrees)x(13.5m) = 1.125m or 1-1/8mFor a 30 rad rotation (rad=radians) , the wagon will have moved forward a multiple of the wheel's circumference that is equal to the multiple that is represented by 30radians. Since the there 2 times Pi radians per 360 degrees, there are 2xPi radians per circumference.Thirty radians (in terms of circumference) = (number of radians)/radians per one circumference) =(30 radians)(1 circumference/2 x Pi radians) =15/Pi circumferencesDistance moved = (multiple of circumference represented by 30 radians)x(circumference)= (15/Pi circumferences)x(4.3m x Pi) = 15x4.3 m = 64.5mFor 30 revolutions, the wagon will have moved forward 30 times the wheel's circumference because one revolution is equal to one circumference.Thirty revolutions = number of revolutions x (number of circumferences/revolution) = 30 rev x (1 rev/1 circumference) = 30 circumferencesDistance moved = (30 circumferences)x(13.5m) = 405m

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