The Friction Block Problem

Friction is a force that slows things down.  Sliding friction is caused by two factors, the roughness of the surfaces and the force that presses them together.  The roughness of the surfaces can be measured by dividing the force of friction F_f by the force that presses them together, F_n.  The result is always a fraction or decimal between zero and one, known as the coefficient of friction, m.  If this coefficient is already known (perhaps from a table in an engineering handbook) and the "normal force" (the force that presses them together, F_n) is measurable, then the friction force can be calculated using the formula F_f = mF_n.

The force of friction can also be found by measuring it directly.  If you push or pull an object at constant speed as it slides over a surface, the applied force has to be equal to the force of friction.  If you can measure the applied force, you therefore know the magnitude of the friction force as well.

Goal: To find the acceleration of the block as it slides down the ramp. For this example, the block has a mass m of 20.0 kg. The ramp angle of elevation q  is 30^o. The coefficient of friction m is 0.50.

The main force in the problem is the weight of the block. F_g = mg = (20.0 kg)(9.81 m/s²) = 196 N

But the block is not free to move straight down. It can only slide down the ramp. Therefore, only a part of the weight [the vector component parallel to the sliding surface of the ramp, F_II] can accelerate the block. Friction tries to hold it back, but friction [F_f = mF_n] is proportional to the perpendicular part of the weight [the normal force, F_n].

So, after calculating the weight, the next step is to calculate the components. Then calculate the force of friction, F_f, and the net force on the block F_NET.

F_n = F_gcosq = 196 N cos(30^o) = 196 N (0.8660) = 170 N

F_II = F_wsinq = 196 N sin(30^o) = 196 N (.5000) = 98 N

F_f = mF_n = (0.50)(170 N) = 85 N

F_NET = F_II - F_f = 98 N - 85 N = 13 N

If we wish to calculate the the acceleration of the block down the ramp, use Newton's Second Law, a = F_NET/m.

a = F_NET/m = (13 N)/(20 kg) = 0.65 m/s²

If we wish to know the final velocity, or the distance covered or an amount of time, we use the formulas from Chapter 2 of our text.