How are frictional forces measured?

Answer 1

When two imperfectly smooth objects slide against one another, a force known as friction is created that always acts against the motion and slows it down in the absence of other forces.

A typical textbook problem in physics is to determine the force of friction when one object (say, a wooden block) slides horizontally across some surface (like a table) and it is pushed against this surface by its weight (force of gravity). A variation is a similar problem, but the surface is not horizontal, but rather a slope of some angle. These two factors are the main determinants of the force of friction.

The coefficient of friction, which measures the force of friction between two objects made of specific materials per unit of pressure and is determined experimentally, is used by physicists to account for the factor of material that objects are made of, as opposed to the pressure force, which can be used to measure how tightly the objects are pushed against each other.

Now, knowing the pressure #F_p# from the physical composition of an experiment and the coefficient of friction #mu_f# of materials involved, we can calculate the force of friction #F_f# as their product: #F_f = mu_f * F_p#

Therefore, we need to know the pressure between the materials and their respective coefficients of friction in order to calculate the force of friction theoretically.

Here is one example of the various ways in which the force of friction can be experimentally determined in the absence of knowledge about the coefficient of friction.

Assume you want to measure the force of friction between a wooden block of mass #M# (#kg#) with the area of its base #S# (#m^2#) that slides across a wooden table. We can start moving this block at some initial speed #V# (#m/sec#) and then let it go by itself until the friction stops it. For instance, the block stops after time #T# (#sec#) after we let it go.
It stops because the friction force #F# stops it acting against the movement, decelerating from speed #V# to #0# during time #T#. We can now determine the degree of deceleration #a# from the initial speed to zero: #a=V/T#
Now, knowing the deceleration and mass of the block, we determine the friction force: #F=M*a=M*V/T#
Since we know the mass and area of the base of our block, we can determine the pressure on the table #P# (weight per unit of area): #P=(M*g)/S#
Finally, we can determine the friction coefficient (the friction force per unit of pressure): #mu=F/P=(M*V*S)/(T*M*g)=(V*S)/(T*g)#

The above obtained coefficient of friction is called kinetic since it was measured during the movement of one object against another; incidentally, the coefficient of friction under these conditions does not depend on the mass of the block.

Another type of coefficient of friction is static, which can also be determined experimentally, but that's a different story. Static friction coefficient measures the initial force of friction when the object starts the movement and is usually greater than kinetic, meaning it's more difficult to start the movement then to continue.

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Answer 2

Frictional forces are typically measured using a device called a dynamometer or a force sensor. These devices apply a known force to an object and measure the force required to overcome friction and move the object. The force measured by the dynamometer or force sensor is the frictional force acting on the object.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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