f4 phy concept

1. The mathematical proof is as follows:
Consider the triangle formed by F1, F2 (the dotted line) and the diagonal (F1+F2)
Let a be the angle opposite to the side of the triangle (F1+F2), then by the cosine rule,
(F1+F2)^2 = (F1)^2 + (F2)^2 - 2.(F1).(F2).cos(a) ----------- (1)

Now, resolve the force F2 into two componets, one is along the direction of F1 and the other perpendicular to it.
Thus, the two components are: F2.cos(180-a) and F2.sin(180 -a)
which are respectively equal to: -F2cos(a) and F2.sin(a)

The resultant force Fr is then given, by Pythagoras Theorem, as,
(Fr)^2 = [F1 + (-F2.cos(a))]^2 + [F2.sin(a)]^2
i.e. (Fr)^2 = [(F1)^2 - 2.(F1).(F2).cos(a) + (F2cos(a))^2] + (F2).sin(a))^2
(Fr)^2 = = (F1)^2 - 2.(F1).(F2).cos(a) + (F2)^2
or Fr^2 = (F1)^2 + (F2)^2 - 2(F1).(F2).cos(a)
Compared with equation (1), the resltant force Fr is just equal to the side of the triangle (F1+F2), i.e. the diagonal of the parallelogram

2. (A&B) The car moves forward, but you are at rest . Since you are inside the car, you would be pushed forward by the back of your seat, which is fixed to the car and moves forward with it.

Simply speaking, a brake is a mechanical device which inhibits motion. Most common brakes use friction to convert kinetic energy into heat. Friction brakes are often rotating devices with a stationary pad and a rotating wear surface. Brakes on automobiles store the braking heat in a braking drum or disc while braking and then conduct it to the air gradually.

2012-01-13 23:46:32 補充：
The braking device slows down the rotating wheels of a car by friction. As the speed of rotation of the wheels decreases, the speed of the car also decreases accordingly.

1.把F2以同樣的長度與角度搬去F1的箭頭,再把這一條折線的頭和尾連起來,就能找出F1+F2(diagonal).所以這方法被稱為tip to tail method.但要注意角度和長度的少許誤差對resultant有很大影響2.當車子at rest的時候,我們與車子都是靜者.當車子開始accelerate的時候,我們還是靜者,所以不會move fowards.但是因為座位與我們的friction漸漸加大,而椅背阻止我們向後移,因此我們亦會被帶動,從而成為動者.假如車子突然at rest,我們仍是動者,因此我們仍然會move fowardsBraking就是stop the motion of the wheels suddenly.因為車子是動者,動者常動,所以它仍然會向前衝(就像第2題那樣).而輪胎的設計就是減少與地面的friction.當輪胎不動,自然會增加與地面的friction.由於friction與車子向前衝的力互相抵銷,net force =0 ,所以車子會停下來.

1. Actually, its the same with the 'tip-to-tail' method to calculate total displacement (addition of vectors). I'm afraid I don't know how to prove by mathematical methods, though. It's similar to Pythagora's Theorem, but not restricted to right angles.

2. By Newton's 1st law, a steadily moving car has constant velocity = no force required (friction is neglible in this case). When the car brakes, it requires a force for deceleration. You still tend to move forward, not because of a force applying to the car, but because of your inertia (i.e. related to your mass. A larger mass= larger reluctance to change motion). You tend to maintain your motion to move forward with constant velocity when the car brakes.

A. If the car accelerates forward from rest or from constant velocity, you don't move forward. You move backwards instead. This is also because of your inertia, so you tend to maintain your motion of staying at rest/ moving with constant velocity.

B. Yes, your right. There's no force acting on you when you move forward. You move forward because your inertia forces you too. Inertia is related to your mass, it is not a force.

Braking: A force is applied by the car on the ground to increase the friction to decelerate the car.

Hope this helps!