一堆physics問題,請大家幫下手, 謝謝! (15分)

2008-07-06 7:09 pm
1 )

Use Newton's laws of motion to explain whether or not a net force is acting on the underlined body in each of the following case.if no net force is acting on the body.describe how the forces are balanced .if a net force is acting , explain the origin of the net foce and state its direction.

A ( cricket ball ) which is colliding obliquely with a smooth horizontal ground.


2 )

A car travelling over a hump which is an arc of a vertical circle.Compared with travelling on a level road ,would the passenger feel heavier ,lighter or the same as that when the car passes the top of the hump? Explain your answer briefly.


3 )

A pendulum bob is attached to a string of length L and made to revolve in a horizontal circle.

i) by neglecting any air resistance ,derive the relation between the period P of the motion and the angle (feter)that the string makes wiht the vertical .

ii) state 2 differences between the motion of the bob and a SHM

回答 (1)

2008-07-06 9:01 pm
✔ 最佳答案
1. As no diagram is given, I presume the underlined object is the cricket ball only

It is obvious that a net force is present. The force comes from the impact with the ground and is pointing vertically upward.
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2. The passengers feel lighter.
The reason is because of inertia. The car goes down suddenly along the arc after passing over the highest point. Passengers inside tends to remain at the higest point by inertia, thus exerting less force onto their seats. The normal reaction on each passenger is reduced and the passenger feels less weight.
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3. Let m be the mass of the bob and g be the acceleration due to gravity
By resolving the tension T on the string vertically and horizontally, we have:

Vertically,
T.cos(theta) = mg ----------------- (1)
Horizontally,
T.sin(theta) = m.r.w^2 ------------ (2)
where r is the radius of the circle
w is the angular speed of revolution

But w = 2.pi/P, where pi =3.14159.....
thus, T.sin(theta) = m.r.(2.pi/P)^2 ---------- (3)

(3)/(1): sin(theta)/cos(theta) = (r/g).[2.pi/P]^2

since from geometry, sin(theta) = r/L
i.e. r = L.sin(theta)

thus (3) becomes, sin(theta)/cos(theta) = [L.sin(theta)/g].[2.pi/P]^2
ie. cos(theta) = (g/L).[P/2.pi]^2

first difference: the magnitude of acceleration is constant in a circular motion, but not in the case of SHM

second difference: the speed is constant in circular motion, but varies with time in SHM


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