Physics Forces!

Q1. The force is constant, equals to 18 N, from t = 0 to 8 s
Hence, acceleration = 18/1.9 m/s^2 = 9.474 m/s^2
Velocity at t = 8 s is 9.474 x 8 m/s = 75.79 m/s

The force decreases linearly from t = 8 to 12 s,
hence, the mean force = 18/2 N = 9 N
Mean acceleration = 9/1.9 m/s^2
Increase in velocity = (9/1.9) x (12-8) m/s = 18.95 m/s
Velcoity at t = 12 s is (75.79 + 18.95) m/s = 94.74 m/s

Q2. (a) Based on the given graph, the elevator is descending. The max apparent occurs when the elevator decelerates and comes to a stop, which is indicated between the time t = 30 to 36 s.

Thus from t = 6 to 30 s, the elevator is descending at constant speed. During such time, the apparent weight equals to the real weight.
Hence, the real weight = 700 x (3/4) N = 525 N
Mass of Henry = 525/g kg = 52.5 kg (take g = 10 m/s^2)

(b) Apparent weight from t=0 to 6 s is 700 x (2/4) N = 350 N
Acceleration = (525 - 350)/52.5 m/s^2 = 3.33 m/s^2
Distance travelled = (1/2).(3.33).(6^2) m [ use: s = ut + (1/2)at^2]
= 60 m
Speed at t = 6 s is 3.33 x 6 m/s = 20 m/s

From t = 6 to 30 s,
Distance travelled = 20 x (30-6) m = 480 m

From t = 30 to 36 s,
Deceleration = (700 - 525)/52.5 m/s^2 = 3.33 m/s^2
Distance tracelled = 20 x 6 + (1/2).(-3.33).(6^2) [ s = ut + (1/2)at^2 ]
= 60 m

Therefore, total distance travelled
= (60 + 480 + 60) m
= 600 m

從所有你可以聯想到的東西思考，當你想到 F = ma，這個圖便相當於一個 加速度 a 對時間 t 的圖，而面積便是速度 v 了。Fmax = 18 N，a(max) = 18 / 1.9 = 9.47 m / s^2。面積 = (上底 + 下底)X高 / 2 = ( 8 + 12 ) X 9.47 / 2 = 94.7 米。

2013-09-29 22:13:21 補充：
其實如果從未見過都要識做是要有很深的功夫才成的，多做習題，多見識各種題目類型當然會很有幫助。

Sorry ，上面的單位錯了，應該 是 94.7 m / s 才對。

2013-09-29 22:39:03 補充：
我對 第 2 題 這樣想 F = ma，縱座標軸(垂直) 分為 4 個刻度，相當於 700 N，每個刻度為 700 / 4 = 175 N。橫座標每個刻度為 6 秒，要假設 0 秒到 6 秒， a = 0，(這個假設似乎免強，但若不如此假設便無從得知 Henry 的 mass 了。Henry 的 mass 做成 350 N 的重力，所以 m = 700 / g = 700 / 9.8 = 71.4 kg。

2013-09-29 22:54:42 補充：
從 6 秒至 30 秒為一個等加速度運動 constant acceleration motion
F = 525 - 350 = 175 N
175 = (71.4)a
a = 2.45 m/s^2
S = Vo t + 0.5at^2 = 0 + 0.5(2.45)(30-6)^2 = 706 m

第 30 秒時的速度 =
V(30) = 0 + at = 0 + (2.45)(24) = 58.8 m/s

2013-09-29 22:58:50 補充：
第 30 至 36 秒，用以加速的力為 350 N，a = 4.9 m / s^2
S = Vo t + 0.5at^2 = 58.8 X 6 + 0.5(4.9)(6)^2 = 441 m

總位移 = 441 + 706 = 1147 m

1147 / 3 = 382 層樓，再加上在 50 樓入電梯，邊有大廈咁高架？