Problem about finding the work done by friction force

[sample5]

Homework Statement

A block of mass M=3.4 kg is dragged over a horizontal surface by a force F=20.0 N. The block is displaced a distance d=17.0 m, the friction force Ff is 3.3 N. What is the work done by the friction force?

Homework Equations

Ff=μkFn

The Attempt at a Solution

I solved a problem before this one in finding the applied force but this one is very confusing to me. I have no idea where to even start. Thank you!

 

[himanshu07]

Work done by friction is always negative. The work done by a constant force is always the dot product of the force multiplied the displacement whether or not the force is the cause of the displacement. So the work done would be -3.3*17 = -56.1 Joules.

 

[danielakkerma]

Why don't we start with recalling how to calculate the work done by any Force?
$\Large W = \int \vec{F} \cdot d\vec{r}$
We can reduce this to simply:
$\vec{F}\cdot{\vec{x}}$
Now the rest is pretty straightforward in your case.
Hope that takes care of the confusion,
Daniel

 

[sample5]

Thank you so much!

 

[rwisz]

I would approach this problem by first understanding the concept of work done by a force. Work is defined as the product of force and displacement in the direction of the force. In this case, the friction force is acting in the opposite direction of the displacement, so the work done by friction will be negative.

To calculate the work done by friction, we can use the equation W = Ff * d, where W is the work done, Ff is the friction force, and d is the displacement. In this problem, we are given the values for Ff and d, so we can simply plug them in to find the work done by friction.

W = (3.3 N) * (17.0 m)
W = -56.1 J

Therefore, the work done by friction is -56.1 Joules. This negative sign indicates that the friction force is acting in the opposite direction of the displacement, and thus, is doing negative work.