# Another seemingly easy forces question

• Element1674
In summary, a block with a coefficient of kinetic friction of 0.15 is pushed with a 150N horizontal force and accelerates at 2.53m/s^2. To find the mass of the block, a system of equations must be used. After accounting for the direction of the forces, the correct answer is 37.5kg, rounded to 2 significant figures. However, some sources may round this answer up to 38kg. Significant figures should be taken into account when solving problems, with 2 significant figures being the most accurate representation in this scenario.
Element1674
Posting this from my phone, apologies.
"A block is pushed across a horizontal surface with a coefficient of kinetic friction of 0.15 by applying a 150N horizontal force. If the block accelerates at 2.53m/s^2 find the mass of the block."

I don't even know where to start. I know the force applied, acceleration and kinetic friction coefficient. I can't use Fnet=ma or Fnet=sum of all forces because I don't have the mass or Fnet. I can't calculate friction without mass (since normal force must be equal to gravity in this scenario, and is there equal to mg). I've drawn a fBD but that didn't really help. Can I get a hint on where to start? Perhaps a system of equations?

Element1674 said:
Posting this from my phone, apologies.
"A block is pushed across a horizontal surface with a coefficient of kinetic friction of 0.15 by applying a 150N horizontal force. If the block accelerates at 2.53m/s^2 find the mass of the block."

I don't even know where to start. I know the force applied, acceleration and kinetic friction coefficient. I can't use Fnet=ma or Fnet=sum of all forces because I don't have the mass or Fnet. I can't calculate friction without mass (since normal force must be equal to gravity in this scenario, and is there equal to mg). I've drawn a fBD but that didn't really help. Can I get a hint on where to start? Perhaps a system of equations?

Yes. A system of equations. Write the equations down in terms of the unknown mass 'm' and try to solve for it.

Yeah I can't quite seem to get it even knowing that. I tried using:
Fnet=ma and Fnet= Ff+Fa
Since they both equal Fnet, they must be equal:
Ma=Ff+Fa
Ma=(mu)mg+Fa
Then I get stuck. I tried rearranging and factoring out mass and I get 58kg (the answer is 38kg)

Element1674 said:
Yeah I can't quite seem to get it even knowing that. I tried using:
Fnet=ma and Fnet= Ff+Fa
Since they both equal Fnet, they must be equal:
Ma=Ff+Fa
Ma=(mu)mg+Fa
Then I get stuck. I tried rearranging and factoring out mass and I get 58kg (the answer is 38kg)

You need to keep track of the direction of the forces. Do the frictional force and the applied force both point in the same direction as the acceleration?

Element1674 said:
Yeah I can't quite seem to get it even knowing that. I tried using:
Fnet=ma and Fnet= Ff+Fa
Since they both equal Fnet, they must be equal:
Ma=Ff+Fa
Ma=(mu)mg+Fa
Then I get stuck. I tried rearranging and factoring out mass and I get 58kg (the answer is 38kg)
Maybe you're confusing yourself by using two symbols for the same mass. All you have to do is solve your equation for $m$. Also be careful of the signs of the forces.

Well acceleration and the force applied are in the same direction. Friction is opposite to that. I don't understand how that changes my calculations though :/

Element1674 said:
Well acceleration and the force applied are in the same direction. Friction is opposite to that. I don't understand how that changes my calculations though :/

It would change ma=mu*m*g+Fa to ma=Fa-mu*m*g. That's a difference.

Ok yes I did that and I got 56kg as an answer. Still incorrect :/

Element1674 said:
Ok yes I did that and I got 56kg as an answer. Still incorrect :/

Put the numbers in and show how you got it. That's not what I get.

Wait are you getting 37.485...kg? I tried agAin and that's what I got

Element1674 said:
Wait are you getting 37.485...kg? I tried agAin and that's what I got

Element1674 said:
Wait are you getting 37.485...kg? I tried agAin and that's what I got
Yes, but you have too many significant figures.

Yay I got it! :) thank you so much!

With significant figures it is 37 right? I think the textbook just rounded wrong

Element1674 said:
With significant figures it is 37 right? I think the textbook just rounded wrong

Depends exactly what you use for g. If you use 9.8m/s^2 you get 37.5kg. Round up, round down? Not really important.

Element1674 said:
With significant figures it is 37 right? I think the textbook just rounded wrong
You could probably get away with 37.5, since the acceleration has 3 figures, the the force has 3, too, arguably.

The blocks acceleration is 2.53m/s^2 which is three significant figures so an answer of 37.5kg is correct. Just don't forget the correct units.

Oh ok. I've learned significant figures differently. 0.15 (the coefficient of friction, can't scroll up and see but i think that's the value) has 2 significant figures and so does the force (150N). The acceleration has 3 but you go by the least significant term so it has 2 in the end

Element1674 said:
Oh ok. I've learned significant figures differently. 0.15 (the coefficient of friction, can't scroll up and see but i think that's the value) has 2 significant figures and so does the force (150N). The acceleration has 3 but you go by the least significant term so it has 2 in the end

You said the book gave 38kg. So they must be rounding 37.5kg up to 38kg. This is really all much less important than getting the physics right.

The force thought with 150N has three significant figures. Leading zeros are not included in significant figures but trailing zeros are. The right answer was found but on a test it is always best to account for significant figures and I have always been expected too. Here is a link on a brief overview of significant figures.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html

I am getting so confused. I will leave it as 2 signficant figures. Thanks all

Element1674 said:
Oh ok. I've learned significant figures differently. 0.15 (the coefficient of friction, can't scroll up and see but i think that's the value) has 2 significant figures and so does the force (150N). The acceleration has 3 but you go by the least significant term so it has 2 in the end
You are correct. I said you could "get away with" using 3 figures because there is a little bit of wiggle room, but strictly you should only use 2 here.

SpaceDreamer said:
The force thought with 150N has three significant figures. Leading zeros are not included in significant figures but trailing zeros are.
That is not exactly correct; trailing zeros on integers are ambiguous. That is why scientific notation is preferred; trailing zeros after the decimal point are significant.

## 1. What are the different types of forces?

The four main types of forces are gravity, electromagnetic, strong nuclear, and weak nuclear. Gravity is the force that pulls objects towards each other, electromagnetic force is responsible for interactions between charged particles, strong nuclear force holds the nucleus of an atom together, and weak nuclear force is responsible for radioactive decay.

## 2. Can you explain Newton's Laws of Motion?

Newton's Laws of Motion are three basic principles that describe the relationship between an object's motion and the forces acting on it. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

## 3. How do forces affect an object's motion?

Forces can cause an object to change its motion in different ways. A force can either cause an object to start moving, speed up, slow down, or change direction. The larger the force, the more it will affect an object's motion.

## 4. What is the difference between weight and mass?

Weight is a measure of the force of gravity acting on an object, while mass is a measure of the amount of matter in an object. Weight can vary depending on the strength of gravity, but mass remains constant. Mass is measured in kilograms, while weight is measured in newtons.

## 5. How do forces interact with each other?

Forces can interact with each other in three ways: they can cancel each other out, they can add together, or they can act in different directions. When forces act in opposite directions with the same magnitude, they cancel each other out. When forces act in the same direction, they add together. When multiple forces act on an object in different directions, the net force is the combination of all the forces acting on the object.

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