Stuck on this physics question
A book has a mass of 400 g. When you slided the book against the floor with 5 N, it accelerated at the rate of -1.5 m/s2. What would the coefficient of friction between the book and the floor be?
Summary:
m = 0.4 kg
F = 5 N
a = -1.5 m/s2
______________
μ = ?
Formulas:
Ff = μFN
FN = -mg
F = ma
I don't understand this clause: "it accelerated at the rate of -1.5 m/s2"
Did the book go backward or not even move at all?
And I have no clue about the force of friction.
So I can't solve this and I need help in solving this question.
Thanks in advance.
P.S: I've been doing quiz on this site: http://www.easyphysics.net/ch4/ch4q.htm - Question 6
Summary:
m = 0.4 kg
F = 5 N
a = -1.5 m/s2
______________
μ = ?
Formulas:
Ff = μFN
FN = -mg
F = ma
I don't understand this clause: "it accelerated at the rate of -1.5 m/s2"
Did the book go backward or not even move at all?
And I have no clue about the force of friction.
So I can't solve this and I need help in solving this question.
Thanks in advance.
P.S: I've been doing quiz on this site: http://www.easyphysics.net/ch4/ch4q.htm - Question 6
Last edited on
It's been ages (almost 20 years) since I last solved such problems, but AFAIR you can construct a force diagram (free body diagram) of the body. Then form the equation, the net horizontal force on the body shall be equal to m*a.
As for the acceleration being negative, IMO it is impossible unless the floor is tilted or the book was given an initial velocity by an extra impulse.
5 - friction = m*a. friction = mu * m*g. Hence, mu = (5 - m*a) / (m*g) |
As for the acceleration being negative, IMO it is impossible unless the floor is tilted or the book was given an initial velocity by an extra impulse.
Last edited on
First of all , I would suggest you to ask these type of questions on a site like http://physicsforum.com , you would get answered quickly ,
on this forum , very few users go to lounge and only a fraction of them would bother to answer a physics question.
Now to your question ,
A negative acceleration means the velocity is decreasing.
You are given the resultant acceleration , one of the two forces are given , solve for the second I.e. the frictional force and from that you solve for \mu.
p.s. I got a minute late.
on this forum , very few users go to lounge and only a fraction of them would bother to answer a physics question.
Now to your question ,
A negative acceleration means the velocity is decreasing.
You are given the resultant acceleration , one of the two forces are given , solve for the second I.e. the frictional force and from that you solve for \mu.
p.s. I got a minute late.
Last edited on
The answer on that site is wrong. (I think the maker accidentally adjusted grams to kilograms one-too-many decimal places. I also don't know how he got the second digit... no rounding accounts for it.)
The net force Fnet is the sum of all forces on your object. The initial push was F=5 N. The force of friction Ff opposes it (which accounts for the negative acceleration -- the box is slowing down as it goes). So:
Fnet = F - Ff
You also know the mass of the object (m=0.4 kg) and the resulting acceleration of your object (a=-1.5 m/s2). Hence:
Fnet = ma
Substitute μFN for Ff and solve for μ.
A lot of physics problems require you to start by drawing pictures (like abish suggests):
^ FN
|
+-----+
Ff <-----| |------> F
+-----+
=============|=============
v Fg
m = 0.4 kg
a = -1.5 m/s2
Next, you need to relate things. You have done a good thing by making yourself a list of information you have. Newton's Laws apply heavily in nearly every problem you do. Find forces that equal (like FN and Fg) and when there is disparity (like F and Ff).
BTW, the force of friction is usually written with a lowercase, curvy ƒ.
Also, there are two different kinds of friction - static (not moving, ƒs) and kinetic (moving, ƒk). This problem obviously deals with ƒk. Likewise, the coefficient of friction μ is different for each one. (μs is almost always larger than μk. That's why it is harder to get something to start moving than it is to keep it moving.)
Oh, finally, just in case you aren't, get used to writing the units of measure with your data during your calculations. Knowing that N = kg m/s2 will help you remember that your given value in grams needs some adjustment, particularly if you wind-up with some wonky units somewhere. (Oh, and μ doesn't technically have units, but you'll still get some wonky stuff with it anyway in later equations you mess with.)
Hope this helps. Don't get discouraged. Physics really is a lot of fun!
[edit] Fixed typo
The net force Fnet is the sum of all forces on your object. The initial push was F=5 N. The force of friction Ff opposes it (which accounts for the negative acceleration -- the box is slowing down as it goes). So:
Fnet = F - Ff
You also know the mass of the object (m=0.4 kg) and the resulting acceleration of your object (a=-1.5 m/s2). Hence:
Fnet = ma
Substitute μFN for Ff and solve for μ.
A lot of physics problems require you to start by drawing pictures (like abish suggests):
^ FN
|
+-----+
Ff <-----| |------> F
+-----+
=============|=============
v Fg
m = 0.4 kg
a = -1.5 m/s2
Next, you need to relate things. You have done a good thing by making yourself a list of information you have. Newton's Laws apply heavily in nearly every problem you do. Find forces that equal (like FN and Fg) and when there is disparity (like F and Ff).
BTW, the force of friction is usually written with a lowercase, curvy ƒ.
Also, there are two different kinds of friction - static (not moving, ƒs) and kinetic (moving, ƒk). This problem obviously deals with ƒk. Likewise, the coefficient of friction μ is different for each one. (μs is almost always larger than μk. That's why it is harder to get something to start moving than it is to keep it moving.)
Oh, finally, just in case you aren't, get used to writing the units of measure with your data during your calculations. Knowing that N = kg m/s2 will help you remember that your given value in grams needs some adjustment, particularly if you wind-up with some wonky units somewhere. (Oh, and μ doesn't technically have units, but you'll still get some wonky stuff with it anyway in later equations you mess with.)
Hope this helps. Don't get discouraged. Physics really is a lot of fun!
[edit] Fixed typo
Last edited on
I did the calculations and got the wrong answers according to the quiz.
So I found that in order to get the correct answer, you need to change 5N to .5N, unless I am doing something else wrong and this is just a coincidence.
.5 - μ*.4*9.8 = -.4*1.5
μ = ( .5 + .4*1.5 ) / ( .4*9.8 ) = 65/392, about .17 which the quiz accepts as the correct answer.
So I found that in order to get the correct answer, you need to change 5N to .5N, unless I am doing something else wrong and this is just a coincidence.
.5 - μ*.4*9.8 = -.4*1.5
μ = ( .5 + .4*1.5 ) / ( .4*9.8 ) = 65/392, about .17 which the quiz accepts as the correct answer.
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The quiz lists "0.15" as the correct answer, but I didn't read all the js in there, so I guess it is allowing some degree of error?
Oh yeah. Calculator error. I had 4 instead of .4, which I tried initially to try and find where the problem's mistake was, then I accidentally left it as 4 when I tried .5 instead of 5.
Last edited on
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