General Physics -- Problem Set #1

Question #6 -- paper roll

Figure 4: Roll dispenser for problem 6

Extra design-work apparently went into making these units so that the paper would not roll off too freely! Question #6 asks you to find the frictional torque caused by the pressure plates on the two sides of the roll (double the torque of one), and balance it against the maximum torque which can be produced by pulling on the paper without it tearing at the perforations. As the roll gets smaller, the radius from the core centre gets smaller, and the same maximum pulling force from the paper produces less and less torque. Finally that pulling torque is not sufficient to overcome the friction force, even when the pull is at it's greatest value -- the tearing tension.

<--close-up of unit, showing leaf springs which press against sides of paper core within the roll

The issue of doubling the resistance torque because of having two friction surfaces doesn't depend on increasing the force -- just the number of surfaces involved. My office chair has tilt-back adjustments, which use a stack of interleaved plates, one set attached to the back, and the other set bound to the base of the chair. A long spring-loaded bolt passes through the stack, so that when the adjustment lever is flipped up, all pressure on the stack is released, and the chair back can be moved; when the lever is flipped down, the spring presses on the whole stack and friction acting between the 18 meeting faces of the stack provides enough friction to hold the chair back in the set position. Same principles as your problem-set question #6.

Close-up of friction plates used to bind tilting chair-back at any chosen position