Question

Many physical properties, such as force and mass, cannot be measured directly. Rather, some other physical property is measured and the desired physical property computed from the results. For example, a bathroom scale does not actually measure mass or \"weight,\" but rather the compression distance of a spring. The numerical values on the scale are calibrated from the compression distance using basic physics principles such as Newton\'s second law. Coefficients of friction cannot be measured directly. In this problem, we are going to learn how we can indirectly measure the coefficient of kinetic friction between two surfaces by directly measuring the expansion of a spring. Consider a 2.12 kg block that is dragged by a spring on a (relatively) frictionless horizontal surface at constant velocity. Suppose the block reaches a rough patch and the spring stretches by 3.25 cm. Compute the coefficient of kinetic friction μ between the block and the rough patch if the spring has a force constant of 172.0 N/m.

Answer 1

Answer:

u =0.269

Explanation:

To find the coefficient of friction we know the following formula

$F_{f} = uN$

Where

$F_{f}$ = Force of Friction

$u$ = Coefficient of Friction

$N$ = Normal Force

Thus we first find the Normal force (N). Remember that the Normal force is perpendicular to the surface, and is equal to the opposing component of Weight (W). Since the surface here is horizontal, then the Normal force will be equal to the Weight.

$N = mg\\ N = (2.12)(9.8)\\ N = 20.776 N$

Now we find the Force on the spring that caused the extension of 3.25cm or 0.0325m

$F_{f} = ke$

Where

$F_{f}$ = Force of Friction

$k$ = Force Constant

= extension

Hence

$F_{f} = ke\\ F_{f} = (172)(0.0325)\\ F_{f} =5.59N$

Now to find the coefficient of friction we use the first formula

$F_{f} = uN\\ 5.59 = u(20.776)\\ u =0.269$