Determining Friction of Table with 100g, 75cm, 2s

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In summary, the conversation discusses how to determine the friction of a table based on the mass, displacement, and time of a cart moving along it. Two approaches are suggested, one using equilibrium and the other using equations of motion. The formula S = (1/2)*a*t*t is used to find the acceleration, and then the force of friction is determined by solving for F. This force is also equal to mu * Mg, where mu is the coefficient of friction and Mg is the weight of the suspended mass. The normal force and friction force are related by the constant of proportionality mu, and the applied force must overcome both the frictional force and the inertial forces of both masses.
  • #1
PhysicsAdvice
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1. A cart travels along a smooth table. The cart moves as a result of a suspended mass attached to a pulley that pulls the cart towards the end of the table. If the mass, displacement and time from start to finish are know, how can you determine the friction of the table?

I think you require acceleration for later on so use v=d/t and then a=v/t to find the acceleration. Then maybe use Fnet=ma or Fnet=Ff + Fapp, what is the applied force equal to and how would you determine it?

Numbers: 100g suspended weight. Distance of 75cm, total time of 2 seconds.
 
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  • #2
Thoughts? It would help a lot :)
 
  • #3
Draw a FBD.

I will give a general approach and a specific approach. In both these ignore rotational inertia of pulley

General approach: (better use this aid for solving)

There are masses M (on table) and m(dangling from pulley).

Consider equilibrium of each block. Find the forces acting.

For eg: the table block has inertial force M*a, frictional force F and string tension T

The mass m has inertial force m * a (note that the strings are assumed to be un extensible) and string tension T. Note that string tensions are the same as there is no friction to alater the tension.


Specific approach:
If you look closely, the gravitational force of mass m is pulling the mass M and m

So the applied force of mg is overcoming the inertial force Ma + ma + frictional force

(M + m)*a + F = m*g ---- (1)

a and F are unknowns

We also know the dispalcement of cart "S", time taken to reach the edge "t"

Use the equation S = (1/2)*a*t*t to find "a"
Put that "a" in (1) and find F

Now F = mu * Mg

mu = F/Mg
 
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  • #4
Thanks, I'm pretty sure I understand. So the M (mass of cart) multiplied by a +force of friction= mass of suspended weight multiplied by gravity. After finding acceleration and plugging everything in you can find F which is the force of Friction, correct?
 
  • #5
PhysicsAdvice said:
Thanks, I'm pretty sure I understand. So the M (mass of cart) multiplied by a +force of friction= mass of suspended weight multiplied by gravity. After finding acceleration and plugging everything in you can find F which is the force of Friction, correct?

Yes, but since both masses are accelerating at the same value, you must add both M and m.

so it is like this:

the ( M (mass of cart) + mass of block hanging ) multiplied by a +force of friction= mass of suspended weight multiplied by gravity
 
  • #6
great, got it. Thanks !
 
  • #7
Sorry to bother you again but is mg= to the normal force? as I know Fn=fg=mg and Ff=mu(Fn), but you said mg is the fapp, so in this case is Fn also Fapp?
 
  • #8
PhysicsAdvice said:
Sorry to bother you again but is mg= to the normal force? as I know Fn=fg=mg and Ff=mu(Fn), but you said mg is the fapp, so in this case is Fn also Fapp?

Normal force Fn is the reaction force due to the mass M and "g". (weight of the cart)

The friction force is proportional to the Normal force, the constant of proportionality is the "mu". The applied force has to overcome BOTH the frictional force + inertial forces (M+m)*a
 

1. How do you determine the friction of a table using 100g, 75cm, and 2 seconds?

The friction of a table can be determined by using the formula μ = F/mg, where μ is the coefficient of friction, F is the force of the object (100g), m is the mass of the object (100g/1000 = 0.1kg), g is the acceleration due to gravity (9.8m/s²), and 75cm is converted to meters (75cm/100 = 0.75m). Plugging these values into the formula gives us a coefficient of friction of μ = F/mg = (0.1kg * 9.8m/s²)/0.75m = 1.31.

2. Why is it important to use a standard mass and distance when determining friction?

Using a standard mass and distance when determining friction allows for consistency and accuracy in the results. It also allows for easier comparison between different surfaces or objects.

3. How does the time of the object's movement affect the determination of friction?

The time of the object's movement does not directly affect the determination of friction. However, a longer time may result in a more accurate measurement as it allows for the object to reach a steady speed, reducing the effects of any initial acceleration or deceleration.

4. Can the coefficient of friction change over time?

Yes, the coefficient of friction can change over time due to factors such as wear and tear on the surface, temperature changes, or the addition of lubricants. It is important to regularly retest the friction of a surface to ensure accuracy in measurements.

5. How does the surface of the table affect the determination of friction?

The surface of the table can greatly affect the determination of friction. A rougher surface will generally result in a higher coefficient of friction, while a smoother surface may result in a lower coefficient of friction. It is important to note the type of surface when comparing friction measurements.

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