SCIENCE: Physics - Mechanical work (constant force)

Work

- amount of energy transferred by a force acting through a distance

- Work can be zero even when there is a force


W = (F cos A) * d


where:

W = mechanical work done

F = constant force applied

A = angle between F and d

d = distance travelled as a result of the application of force



1. Force and distance on the same line

A toy cart is placed in a rail that is flat on a table. A pulling force of 10 N is applied resulting in a distance of 2 m travelled by the toy cart. Calculate the work done.


find:

W = work done


given:

F = 10 N

A = 0 degrees

d = 2 m


solution:

W = (F cos A) * d

W = (10 * cos 0) * 2

W = (10 * 1) * 2

W = 20 N m



2. Force is at an angle with the direction of motion

If the force is applied with an angle of 30 degrees, calculate the work done.


find:

W = work done


given:

F = 10 N

A = 30 degrees

d = 2 m


solution:

W = (F cos A) * d

W = (10 * cos 30) * 2

W = 17.3 N m



3. The rail is at an angle of 15 degreees with the table


If (in problem #2) the toy cart is moved down, calculate the work done.


find:

Wd = work done if the toy cart is moved down


given:

F = 10 N

a1 = 30 degrees, angle of the force

a2 = 15 degrees, angle of the rail

d = 2 m


solution:

reference is the rail --> direction of the displacement


A = a1 + a2

A = 30 + 15

A = 45 degrees


Wd = (F cos A) * d

Wd = (10 * cos 45) * 2

Wd = 14.1 N m



If (in problem #2) the toy cart is moved up, calculate the work done.


find:

Wu = work done if the toy cart is moved up


given:

F = 10 N

a1 = 30 degrees, angle of the force

a2 = 15 degrees, angle of the rail

d = 2 m


solution:

reference is the rail --> direction of the displacement


A = a1 - a2

A = 30 - 15

A = 15 degrees


Wu = (F cos A) * d

Wu = (10 * cos 15) * 2

Wu = 19.3 N m