Mass of block given μK and Force?

1. Nov 15, 2012

Ace.

1. The problem statement, all variables and given/known data

A student pushes a block with 240 N of force across a horizontal surface with a coefficient of kinetic friction of 0.4. The block accelerates at a rate of 0.88 m/s2. Find the mass of the block.

2. Relevant equations

μK = FK / FN
F=ma

3. The attempt at a solution

My first attempt was to figure out mass using F=ma

m = f/a
= 240 N / 0.88 m/s2
= 272.7 kg​

but this is not taking into account the kinetic friction...

So what I did was

FK = μK x FN
= 0.4 x (272.7 kg x 9.8 m/s2
= 1069.1 N​

I know I'm doing this wrong and I need to know how to derive at net force to find acceleration

2. Nov 15, 2012

Staff: Mentor

To use ƩF = ma you must include all the forces.

Instead, just call the mass "m" and set up your equation using the net force. Then you can solve for the mass. What's the friction force in terms of "m"?

3. Nov 15, 2012

Ace.

μK = FK / FN
FN = FK / μK
mg = FK / μK
m = (FK / μK) / g

Like this?

4. Nov 15, 2012

Staff: Mentor

No. (That won't work, since FK is proportional to the mass, so your equation ends up being m = m.)

Use ƩF = ma. First work on the forces. There are two forces acting. What are they?

5. Nov 15, 2012

Ace.

force applied of 240 N and kinetic friction

I can't find magnitude of kinetic friction because I cannot find Force normal.

6. Nov 15, 2012

Staff: Mentor

Good.

If the mass is "m", what's the weight?

7. Nov 15, 2012

Ace.

weight = 9.8m

8. Nov 15, 2012

Staff: Mentor

Good. So now you have the normal force. Keep going.

9. Nov 15, 2012

Ace.

μK = FK / FN
FK = μK × FN
FK= 0.4 x 9.8m

I have 2 unknowns?

10. Nov 16, 2012

Staff: Mentor

Good.

The only unknown is the mass, which is what you are trying to find.

Keep going. What is ƩF?

11. Nov 16, 2012

Ace.

Fapplied = 0.88m

just guessing here:
Fnet = FA [fwd] + Ff [bwd]
Fnet = FA [fwd] - Ff [fwd]
Fnet = 0.88m - (0.4 x 9.8m)

12. Nov 16, 2012

Staff: Mentor

The applied force is given as 240 N.

This is good.
Fix this and then use Fnet = ma.

13. Nov 16, 2012

Ace.

Fnet = 240 - (0.4 x 9.8m)
= 240 - 2.92m​

Still don't get what I need to do next?

14. Nov 16, 2012

Staff: Mentor

Apply Newton's 2nd law: Fnet = ma

15. Nov 16, 2012

Ace.

240 - 2.92m = 0.88m
240 = 0.88m + 2.92m
240 = 3.8m
m = 63 kg

16. Nov 16, 2012

Staff: Mentor

That's the right idea. But I think you made a mistake earlier (probably a typo):

Fix that, resolve your equation, and you'll have the correct mass.

17. Nov 16, 2012

Ace.

Fnet = 240 - (0.4 x 9.8m)
= 240 - 3.92m

240 - 3.92m = 0.88m
240 = 0.88m + 3.92m
240 = 4.8m
m = 50 kg

wohooooooo thanks a lot!

18. Nov 16, 2012

Yay!