Home > Physics > Frictional Forces

An object with a mass of # 3 # #kg# is lying on a surface and is compressing a horizontal spring by #10 # #cm#. If the spring's constant is # 9# #kgs^-2#, what is the minimum value of the surface's coefficient of static friction?

Answer 1

Elena Albarran

The frictional coefficient #mu=0.03#.

(convert the distance to SI units: #10# #cm# = #0.1# #m#)

The force exerted by the spring is given by:

#F=kx=9xx0.1=0.9# #N#

Since the object is stationary, this force applied by the spring must be being balanced by the frictional force.

The frictional force is given by:

#F_"frict"=muF_"normal"#

And the normal force is the gravitational force:

#F_"normal"=mg=3xx9.8=29.4# #N#

Rearranging:

#mu=F_"frict"/F_"normal"=0.9/29.4=0.03#

(frictional coefficients do not have units)

(side note: I keep saying that #kgs^-2# is an odd unit for spring constant. It is correct, but so is #Nm^-1#, and the latter makes is easier to understand what is going on in most contexts.)

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Julia Aguilar

The minimum value of the surface's coefficient of static friction is 0.3.

By signing up, you agree to our Terms of Service and Privacy Policy

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.