Author: mrchuakh

6.2.2 Disastrous Turn and Disastrous Spin

Concept Test 1

Answer:

The bio teacher skidded.

The bio teacher chose the inside track (A), presumably thinking that it is safer to stay away from the cliff. Alas, at the SAME SPEED, the inside track with the smaller radius of turn requires a larger centripetal force. (Think Fc=mv2/r) Skidding occurs when friction (between the tyre and the road) is not large enough to provide the required centripetal force.

P.S. It is misleading to think Fc=mrω2 because the two motions do not have the same angular velocity ω.

Concept Test 2

Answer:

The bio teacher went projectile (tangentially btw).

The bio teacher chose an outside chair, the bike accident still fresh in the memory presumably. Alas, at the SAME ANGULAR VELOCITY, the outer path with the larger radius of turn requires a larger centripetal force. (Think Fc=mrω2) The tension (the horizontal component, to be specific) in the cable, which provides the required centripetal force, is thus always larger for the outer chair than the inner chair. Logically, the outer cable should snap first.

P.S. It is misleading to think Fc=mv2/r because the two motions do not have the same linear speed v.

4.3.4 Rotational Equilibrium

In this video, you can see a rigid body, formed by joining two balls, being thrown across the screen. Tracing the trajectory of either ball shows a complicated path. On the other hand, the trajectory of the CM is the familiar parabolic arc of a projectile motion. This shows that an object’s motion can be treated as a translational motion of the CM juxtaposed with a rotational motion about its CM.

3.4.1 Frictional Force

Friction does not oppose motion. Friction opposes relative motion. In fact, when walking, we use friction both to initiate and stop motion.

One useful thing to know about friction is this: the friction between two surfaces increases if the two surfaces are pressed more strongly into each other.

Explanation at xmdemo.wordpress.com/115

When friction is multiplied thousands of times…

Explanation at xmdemo.wordpress.com/097

3.4.1.1 Laws of Friction

  • The frictional force between two stationary surfaces is called the static friction,  fs.
  • The frictional force between two sliding surfaces is called the kinetic friction, fk.
  • It can be shown empirically that between two particular surfaces
    • static friction fs ranges from zero to a maximum value.

0 < fs < μsN

    • kinetic friction fk is constant and independent of speed.

fk = μkN 

    • maximum static friction is larger than kinetic friction.

This video shows clearly how the static friction increases until reaching its maximum value, then drops to the constant kinetic friction.

Unlike drag force, friction is unaffected by the sliding speed. It is also unaffected by the area of the surfaces in contact. All that matters is the material of the two surfaces and how hard they are pressed against each other.