Newton's Third law of motion problem.

[abrowaqas]

Homework Statement

An object is free to move on a table, ex-
cept that there is a constant friction force f
that opposes the motion of the object when
it moves. If a force of 10 N pulls the object
across the table, the acceleration is 2 m/s2. If
a force of 20 N pulls the object across the ta-
ble, the acceleration is 6 m/s2. What is the
force of friction f?

a) 3.33 N
b) 1 N
c) 5 N
d) 10 N
e) none of these

Homework Equations

F= ma
and
F= -F'

and
F= μS where μ= coefficient of static friction

The Attempt at a Solution

i first find the mass in both case

F= 10 N and a= 2m/s/s
so
m= F/a = 10/2
m= 5kg

and again

F= 20N and a= 6m/s/s

so
m= F/a = 20/6
m= 3.33kg

what i do next..
or
either i must go to

F= μ S

please help me to solve it.. how i go further?

 

[Doc Al]

F= 10 N and a= 2m/s/s
so
m= F/a = 10/2
m= 5kg

10 N is the applied force, not the net force. To use Newton's 2nd law you need the net force.

 

[abrowaqas]

then Doc Al

how will i find the net force..
will it be

Fnet = 20+10 = 30N ...
what i do next?

 

[Doc Al]

how will i find the net force..
will it be

Fnet = 20+10 = 30N ...

No. In the first case, what two forces act? One is the applied force of 10 N. What's the other force?

You'll end up with an equation with 2 unknowns.

Then you'll get a second equation, using the second case (with the applied force of 20 N).

You'll solve those two equations for the two unknowns.

 

[asteriatic]

I would approach this problem by first identifying the key variables and principles at play. The key variables in this problem are force, acceleration, and friction. The principle that applies is Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

Using the information given, we can see that the force of 10 N and 20 N are the actions, and the resulting acceleration of 2 m/s2 and 6 m/s2 are the reactions. This means that there must be an equal and opposite force acting on the object to produce these accelerations. This force is the force of friction, which is opposing the motion of the object.

To find the force of friction, we can use the equation F=ma. In this case, the force we are looking for is the force of friction, and the acceleration is the given values of 2 m/s2 and 6 m/s2. We can rearrange the equation to solve for F, which gives us F=m*a.

Plugging in the values for mass (5 kg and 3.33 kg), we can calculate the force of friction for each scenario. For the first scenario, with a force of 10 N and an acceleration of 2 m/s2, the force of friction would be 10 N. For the second scenario, with a force of 20 N and an acceleration of 6 m/s2, the force of friction would be 20 N.

Therefore, the correct answer is d) 10 N.

It is important to note that the force of friction is dependent on the mass of the object, as seen in the different values calculated for the different masses. It is also important to consider the coefficient of friction, which is a constant that depends on the surfaces in contact. In this case, the coefficient of friction is not given, so we cannot calculate the exact value of the force of friction. However, we can confidently say that the force of friction will always be equal and opposite to the applied force, as per Newton's Third Law.