# How do I find the work done for a 100 N downward force?

• haha0p1
In summary: Can you find these for the 100 N force acting downwards?In summary, the work done for the 100 N force acting downwards can be found using the equation W=Fdcostheta, where F is the magnitude of the force and d is the magnitude of the displacement. The component of the force in the direction of the displacement is found by multiplying the force by the cosine of the angle between the force and the displacement vectors. The magnitude of the displacement is given as 0.5m in the problem.
haha0p1
Homework Statement
The figure shows the forces acting on a box that is being pushed up a slope. Calculate the work done by each force if the box moves 0.50m up the slope.
Relevant Equations
Work done= Force×Direction of force
I have found the work done for 100 N, 70 N and 30 N force, but I don't know how to find work for 100 N force that is acting downwards.
Force 70N:
W=F×d = 70 ×0=0 Nm (Force is perpendicular to the distance moved)
100 N force:
W=F×d=100×0.5=50 Nm
30N force:
30×-.5= -15Nm.
Please check whether these answers are right and also tell how to find the work done for 100 N force acting downwards.

haha0p1 said:
Homework Statement:: The figure shows the forces acting on a box that is being pushed up a slope. Calculate the work done by each force if the box moves 0.50m up the slope.
Relevant Equations:: Work done= Force×Direction of force

I have found the work done for 100 N, 70 N and 30 N force, but I don't know how to find work for 100 N force that is acting downwards.
Force 70N:
W=F×d = 70 ×0=0 Nm (Force is perpendicular to the distance moved)
100 N force:
W=F×d=100×0.5=50 Nm
30N force:
30×-.5= -15Nm.
Please check whether these answers are right and also tell how to find the work done for 100 N force acting downwards. View attachment 319614
So far so good, but I see a hint of why you are having difficulties in your Relevant Equations.

The equation for the work done by a force is ##W = \textbf{F} \cdot \textbf{d}## where ##\textbf{d}## is the displacement. Using the definition of the dot product we get ##W = \textbf{F} \cdot \textbf{d} = F d ~ cos( \theta )## where ##\theta## is the (smaller) angle formed when you put the force and displacement tail to tail.

See what you can do with this. (And make sure you know how to do the other three forces this way as well.)

-Dan

haha0p1
The displacement is tangential to the slope. The best approach is to decompose each force into its components tangential to and normal to the slope. The work done is then the product of the tangential component times the displacement.

For the first three forces, this is simple, as these forces are either normal to or tangential to the slope.

You need to decompose the ##100 \ N## force of gravity into the relevant components.

topsquark and haha0p1
Hello. Thanks for replying. I used the equation FdCostheta and found the correct answer. I also used the equation for my other three forces and found the required answers aswell.

Lnewqban
haha0p1 said:
Hello. Thanks for replying. I used the equation FdCostheta and found the correct answer. I also used the equation for my other three forces and found the required answers aswell.
The work done can be defined as the dot product of the force and dislacement vectors:
$$W = \vec F \cdot \vec s = |\vec F||\vec s| \cos \theta = Fs \cos \theta$$Note that ##F \cos \theta## is the component of the force in the direction of the displacement. And ##s## is the magnitude of th displacement.

haha0p1 and topsquark

## What is work done by a force?

Work done by a force is the measure of the energy transferred to an object when a force is applied to it and it moves in the direction of the force.

## How is work done by a force calculated?

Work done by a force is calculated by multiplying the magnitude of the force by the distance the object moves in the direction of the force.

## What are the units of work done by a force?

The units of work done by a force are joules (J) in the SI system and foot-pounds (ft-lb) in the English system.

## How does the angle between the force and displacement affect the work done?

The angle between the force and displacement affects the work done by changing the component of the force that is in the direction of the displacement. The work done is greatest when the force and displacement are in the same direction (0 degrees) and zero when they are perpendicular (90 degrees).

## What is the difference between work done by a force and work done on an object?

Work done by a force refers to the energy transferred to an object by a force, while work done on an object refers to the energy required to move the object against a force. The former is a measure of the effect of a force, while the latter is a measure of the resistance of an object to a force.

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