SAT2 Physics 03 Force (Lecture) with Chinese

SAT2 Physics

(by: Dr. Yu)

Lecture Notes

Dynamics 动力学 (Why things move.)

● What is Force 力?

Contact force 接触力, and field force 超距力 (Action-at-a-distance force).

A force is a vector 矢量.

What is the unit of force? (Think about an apple.) The unit of force is in “Newton”.

● Newton’s first law: The law of inertia 惯性定律.

In the absence of external force, an object at rest remains at rest and an object in motion continues in motion with constant velocity.

The definition of inertia 惯性、惯量 (Look over the dictionary!):

The tendency of an object to resist the attempt to change its velocity is called “inertia” of the object.

● Newton’s second law: F ma =

The definition of mass : (It is actually very profound!)

Mass is a quantitative description of inertia 惯量.

Mass is the ratio of force to acceleration 加速度 (or force per unit of acceleration).

F ma =

F m a

?≡

The unit of mass: 22

/(/)/N m s Ns m = 21 1 /(/)kg N m s ≡

F ma =

? When 0F = ?

0a =

?constant v = ?the Newton’s first law.

● Newton’s third law: The law of action and

reaction 作用、反作用 (Very profound too!)

Whenever one body exerts a force on another, the second body exerts simultaneously on the first a force that is equal in magnitude and opposite in direction to the force of the first on the second.

1221F F →→=-

“You push me and I’ll pus h you (with the same

force)!”

● Some application of Newton’s law:

● Gravitational force 万有引力、重力 (a big topic!!)

The gravitational force near the surface of the earth:

g F ma F mg =?=

, where (according to the

experiments) 29.8 m/s g =

usually, 2?9.8 m/s g j =-

. g

is called the “gravitational accelerati on 重

力加速度”.

The gravitational force per unit mass is called the “gravitational field”.

Because g F mg =

?F g m

=

, the unit of

gravitational field is N/kg.

g F mg =

g F m g

?=

(very profound too)

The gravitational force is also called the “weight” 重力, so the weight is a force.? The unit of weight is in Newton 牛顿, not in kilogram 公斤.

If I say: “The weight of the apple is 0.1 kilogram.”, then I am wrong ！

I must say that the weight of the apple is how much Newton, or that the mass of the apple is how much kilogram.

Suppose that I have an apple with a mass of 0.1 kg, then the weight of the apple (near the surface of the

earth) is 0.1 (kg)9.8 (N/kg)g F m g ==?

=

0.98 N.

● Tension 张力: The tension is force, so the unit

of tension is in Newton.

● Free-body diagram: Extremely important!!

● Normal force 法向力N F

:

The normal force N F

is the component,

perpendicular to the surface of contact, of the contact force exerted by, for example, the surface of a floor or wall, on an object,

preventing the object from entering the floor or wall.

● Equilibrium problems 平衡问题

0net F =

or

0i F =∑

● One block push another

Need to consider the Newton’s 3rd law.

● Atwood’s Machine

● Acceleration of two objects connected to each

other by a cord

● Incline motion 斜面运动

Force of Friction 摩擦力:

● Force of static friction 静摩擦力, coefficient

of static friction s μ

fr s N F F μ≤

● Force of kinetic friction 动摩擦力, coefficient

of kinetic friction k μ

fr k N F F μ=

(The direction of the friction force is always opposite to the direction of motion.)

Usually,

k s μμ<.

● Incline motion with friction

cos fr k N k F F m g μμθ==

● Centripetal Acceleration 向心加速度 2

c v a r

=

Speed: 2r

v T

π=

(T : Period 周期) 224c r a T

π∴=

● Centripetal Force 向心力

● Circular Motion 圆周运动: Horizontal 水平,

Vertical 垂直, etc…

Theory of Gravitation 万有引力理论 或 重力理论:

Newto n’s Theory of Gravitation: (one of the greatest theories in physics)

● Gravitation Force 重力

(the magnitude):2

g GMm

F r =

● Gravitation Field 重力场

(the magnitude):2F GM g m r

≡

= ● Satellite Motion 卫星运动: Distance, Speed, Period,

Gravitation Force

● Space Station 太空站

● The Torque 力矩: r F τ=?

(the cross product 矢量积) What is the direction 方向 of the torque?

(Think about a screw, or bolts and nuts.)

The magnitude 大小 of torque:

sin r F τθ=

, or rF τ⊥= Think about pushing a door, or using a

wrench 扳手.

● The equilibrium 平衡: 0F ∑= (translational 平移的) and 0τ∑=

(rotational 旋转的)

For most of the questions, we have to consider the

rotational equilibrium: 0τ∑=

.

Kinetic equilibrium 动平衡: velocity = constant

Static equlibrium 静平衡: velocity = 0

(for

most of the questions.)

Example: seesaw 秋千、跷跷板 (teeterboard).