Question

A compound machine is sued to lift a car. If you apply a force of 60 N to the machine, it lifts the car with a force of 550 N.

a. What is the mechanical advantage of the machine?

b. The machine has an efficiency of 35%. If you perform 1150 J of work, how much useful work does the machine do?

Answer 1

a) MA=550/60=9.17

b) Wu=1150*0.35=402.5 J

Answer 2

a) 9.167

b) 402.5 J

Step-by-step explanation:

We have a machine, which when applying a force of 60N, it returns 550N.

a) The mechanical advantage of a machine is the number of times that the machine increases an input force.

Mathematically, is the relationship between the output force and the input force.

The mechanical advantage is dimensionless.

In this case, the input force (the force we apply) is 60 N; and the output force (the force that the compound machine exerts) is 550 N.

We solve it this way:

`M.A.=(550N)/(60N) =9.167`

This is the mechanical advantage of the machine in this exercise.

b)In a machine, we define the efficiency as the relationship between the work we receive from the machine, and the work we give to it.

The machine efficiency is a real number between 0 and 1 and is dimensionless.

In this exercise, the efficiency is 35% = 0.35

We solve it this way :

`(WorkWeReceive)/(WorkWeGive)=0.35`

`(WorkWeReceive)/(1150J)=0.35`

`WorkWeReceive=(0.35).(1150J)=402.5J`

We obtain 402.5 J useful work from the machine.