A wheel is used to turn a valve stem on a water valve. The wheel radius is 4 inches and the axle radius is .25 inches.

a. What is the mechanical advantage of the wheel and axle?

b. How much resistance force can be overcome when an effort of 6 lbs is applied to the wheel of the water valve in this problem?

a) The mechanical advantage of the wheel and axle is 16.

Mechanical advantage (MA) of a machine is the ratio of the load to effort

put into the machine or the ratio of the radius of the wheel 'R' to that of the axle

'r'.

MA = R/r

where R = 4 inches,  r = 0.25 inches

MA = 4/0.25 = 16

The mechanical advantage is 16.

b)  The resistant force which has to be overcome is the Load

MA = Load/ Effort

where MA is 16, Effort is 6 lbs, Load = ?

Load = MA × Effort

         = 16 ×6

           = 96lbs

The Load is therefore 96 lbs.

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a. The mechanical advantage (MA) is 16.

b. The value of the resistance force is 96 lbs.

Explanation:

a) Mechanical advantage (MA) of a machine can be define as the ratio of the load overcommed to effort put into the machine. But in the case of wheel and axle, mechanical advantage can be determined by the ratio of the radius of the wheel 'R' to that of the axle 'r'.

                     MA =

R = 4 inches and r = 0.25 inches

So that,

               MA =

                     = 16

Therefore, the mechanical advantage is 16.

b) The resistance force to be overcommed is the load. Thus,

                  MA =

But, MA = 16, Effort = 6 lbs, Load = ?

So that,

              Load = MA × Effort

                       = 16 ×6

                       = 96

The value of load required is 96 lbs.