# Simple machine (inclined plane, lever) – problems and solutions

1.

Which inclined plane have the same mechanical advantage

A. (1) and (2)

B. (1) and (3)

C. (2) and (3)

D. (2) and (4)

Solution

The inclined plane is one of the simple machines. Simple machines are tools that help people do a job. The inclined plane is used to make it easier for humans to raise an object to a certain height.

The mechanical advantage of the inclined plane is the comparison of the length of the incline to the height of the incline.

The mechanical advantage of the incline plane 1 = 50 cm / 30 cm = 5/3

The mechanical advantage of the incline plane 2 = 5 cm / 4 cm = 5/4

The mechanical advantage of the incline plane 3 = 50 cm / 40 cm = 5/4

The mechanical advantage of the incline plane 4 = 5 cm / 3 cm = 5/3

2.

Distance AB = BC = CD = DE, determine the input force that must be given at point E in order for a balanced lever.

__Known :__

AB = BC = CD = DE = l

Distance between output force and fulcrum (a) = l

Distance between input force and fulcrum (b) = 3l

Output force (w) = 900 Newton

__Wanted :__ Force (F)

__Solution :__

The mechanical advantage :

MA = b / a = 3l/l = 3

Magnitude of force :

MA = w / F

F = w / MA

F = 900 Newton / 3

F = 300 Newton

3.

In order for the lever to be balanced then determine the magnitude of its input force.

Solution

**Determine distance between input force and fulcrum ****(****b****) **

__Known :__

Distance between output force and fulcrum (a) = 25 cm

Output force (w) = 480 Newton

Input force (F) = 160 N

__Wanted :__ The distance between input force and fulcrum (b)

__Solution :__

The mechanical advantage :

MA = w / F = 480 N / 160 N = 3

The distance between input force and fulcrum (b)

MA = b / a

3 = b / 25 cm

b = (3)(25 cm)

b = 75 cm

**Determine magnitude of force ****(F) **

__Known :__

Distance between output force and fulcrum (a) = 25 cm – 10 cm = 15 cm

Object’s weight (w) = 480 Newton

Distance between input force and fulcrum (b) = 75 cm

__Wanted :__ Input force (F)

__Solution :__

Mechanical advantage :

MA = b / a

MA = 75 cm / 15 cm

MA = 5

Magnitude of force (F) :

MA = w / F

F = w / MA

F = 480 Newton / 5

F = 96 Newton

In order for the lever to be in a balanced position then input force is reduced 64 Newton (160 N – 96 N).

4. The ratio of the lengths of a and b in figure below is a: b = 1: 2.2. The minimum value of force F to lift the object B with weight of 330 Newtons is …. Newton

A. 100

B. 150

C. 2200

D. 7260

__Known :__

Distance between output force and fulcrum (a) = 1

Distance between input force and fulcrum (b) = 2.2

Weight (w) = 330 Newton

__Wanted :__ Input force (F)

__Solution :__

The mechanical advantage of a lever :

MA = w / F = b / a

*MA = **mechanical advantage**, w = weight, F = input force, b** **= distance between input force and fulcrum, a = distance between **output force and fulcrum*

w / F = b / a

330 / F = 2.2 / 1

330 / F = 2.2

330 / 2.2 = F

F = 150 Newton

The correct answer is B.

5. A student push an object with a force of F from point A to point B, as shown in figure below. If the friction between object and boar ignored, determine the mechanical advantage.

A. 4

B. 5/3

C. 5/4

D. ¾

Known :

Height of inclined plane (y) = 4 meters – 1 meters = 3 meters

Length of horizontal plane (x) = 4 meters

__Wanted:__ Mechanical advantage (MA)

__Solution :__

Calculate the length of the inclined plane using the equation of *Pythagoras* :

R = √3^{2}+4^{2} = √9+16 = √25 = 5 meters

The mechanical advantage of the inclined plane :

KM = R / y

KM = 5 meters / 3 meters

KM = 5/3

The correct answer is B.

6. The mechanical advantage of a lever can be increased by…

A. Shorten the path of the incline

B. enlarge the angle of the incline

C. minimize the angle of the incline

D. reduces the force used to move objects

Solution :

The equation of mechanical advantage of the inclined plane :

__Mechanical advantage = length of inclined plane/height of the inclined plane__

– The mechanical advantage is directly proportional to the length of the inclined plane and therefore the mechanical advantage is enlarged if the length of the incline is enlarged.

– The mechanical advantage is inversely proportional to the height of the inclined plane, therefore, the mechanical advantage is minimized if the height of the inclined plane is enlarged and the mechanical advantage is enlarged if the height of the incline is reduced.

– If the angle is minimized then the height of the inclined plane is reduced. The mechanical advantage is enlarged if the height of the inclined plane is reduced. Hence if the angle is minimized then the mechanical advantage is enlarged.

If the angle is enlarged then the height of the inclined plane is enlarged. The mechanical advantage is minimized if the height of the inclined plane is enlarged. Hence if the angle is enlarged then the mechanical advantage is minimized.

The correct answer is C.