Mass of block given μK and Force?

In summary, the conversation discussed a problem where a student needed to find the mass of a block being pushed with a force of 240 N and experiencing a coefficient of kinetic friction of 0.4 on a horizontal surface. The student first attempted to use F=ma to find the mass but realized they needed to take into account the kinetic friction. They then used ƩF=ma and set up an equation with the net force, which included the applied force and the friction force. After some trial and error, the student correctly found the mass to be 50 kg.
  • #1
Ace.
52
0

Homework Statement



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.

Homework Equations



μK = FK / FN
F=ma

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
 
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  • #2
Ace. said:
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...
To use ƩF = ma you must include all the forces.

So what I did was

FK = μK x FN
= 0.4 x (272.7 kg x 9.8 m/s2
= 1069.1 N​
You are using the incorrect answer from your first attempt.

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
You are using the incorrect answer from your first attempt.

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"?

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

Like this?
 
  • #4
Ace. said:
μK = FK / FN
FN = FK / μK
mg = FK / μK
m = (FK / μK) / g

Like this?
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
force applied of 240 N and kinetic friction

I can't find magnitude of kinetic friction because I cannot find Force normal.
 
  • #6
Ace. said:
force applied of 240 N and kinetic friction
Good.

I can't find magnitude of kinetic friction because I cannot find Force normal.
If the mass is "m", what's the weight?
 
  • #7
Doc Al said:
Good.If the mass is "m", what's the weight?

weight = 9.8m
 
  • #8
Ace. said:
weight = 9.8m
Good. So now you have the normal force. Keep going.
 
  • #9
μK = FK / FN
FK = μK × FN
FK= 0.4 x 9.8m

I have 2 unknowns?
 
  • #10
Ace. said:
μK = FK / FN
FK = μK × FN
FK= 0.4 x 9.8m
Good.

I have 2 unknowns?
The only unknown is the mass, which is what you are trying to find.

Keep going. What is ƩF?
 
  • #11
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
Ace. said:
Fapplied = 0.88m
The applied force is given as 240 N.

just guessing here:
Fnet = FA [fwd] + Ff [bwd]
Fnet = FA [fwd] - Ff [fwd]
This is good.
Fnet = 0.88m - (0.4 x 9.8m)
Fix this and then use Fnet = ma.
 
  • #13
oh wow my bad...

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

Still don't get what I need to do next?
 
  • #14
Ace. said:
oh wow my bad...

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

Still don't get what I need to do next?
Apply Newton's 2nd law: Fnet = ma
 
  • #15
240 - 2.92m = 0.88m
240 = 0.88m + 2.92m
240 = 3.8m
m = 63 kg
 
  • #16
Ace. said:
240 - 2.92m = 0.88m
240 = 0.88m + 2.92m
240 = 3.8m
m = 63 kg
That's the right idea. But I think you made a mistake earlier (probably a typo):

Ace. said:
Fnet = 240 - (0.4 x 9.8m)
= 240 - 2.92m​

Fix that, resolve your equation, and you'll have the correct mass.
 
  • #17
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!:biggrin:
 
  • #18
Yay! :approve:
 

What is the formula for calculating the mass of a block given the coefficient of kinetic friction (μK) and the applied force?

The formula for calculating the mass of a block given μK and Force is:
m = F/μK, where m is the mass of the block, F is the applied force, and μK is the coefficient of kinetic friction.

How do you determine the coefficient of kinetic friction (μK) for a particular surface?

The coefficient of kinetic friction (μK) can be determined by conducting an experiment where a block is pulled or pushed across the surface with a known force and measuring the resulting acceleration. μK can then be calculated using the formula μK = F/m, where F is the applied force and m is the mass of the block.

What are the units for the coefficient of kinetic friction (μK)?

The coefficient of kinetic friction (μK) has no units, as it is a dimensionless value that represents the ratio of the frictional force to the normal force between two surfaces.

How does the mass of the block affect the coefficient of kinetic friction (μK)?

The mass of the block does not directly affect the coefficient of kinetic friction (μK). However, a heavier block may experience a greater normal force, which in turn can affect the coefficient of kinetic friction.

Can the coefficient of kinetic friction (μK) be greater than 1?

Yes, the coefficient of kinetic friction (μK) can be greater than 1. This means that the frictional force is greater than the normal force, resulting in a frictional force that is greater than the applied force. In this case, the block will experience a deceleration rather than an acceleration when a force is applied.

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