關於物理的簡單問題(2)

Tieria

2010-04-03 7:06 am

1. At time t = 0, two cars A and B start moving from rest at the same place. Their velocity-time graphs (v-t graph) are shown in the figure. In the figure, area I is greater than area II. Which of the following statements about their motions is / are correct?
(1) From t = 0 to t = x, the average velocity of A is equal to that of B.
(2) From t = 0 to t = x, the average acceleration of A is equal to that of B.
(3) A is always ahead of B at any time from t = 0 to t = y.
A. (1) and (2) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)
http://i617.photobucket.com/albums/tt257/michaelcoco_/ce09bb70.jpg

2. Two masses M and m (where M > m) are placed on the floor as shown. The arrows (with the number) represent the forces as described. The masses are at rest. Which of the following statements is / are correct?
Force 1 = weight of m
Force 2 = normal reaction acted on m
Force 3 = normal reaction acted on the top of M
Force 4 = weight of M
Force 5 = normal reaction acted on the bottom of M
Force 6 = normal reaction on floor
(1) When considering M and m as a system, forces 1, 4 and 5 should be included in the free body diagram of this system.
(2) Force 2 and 3 form an action-reaction pair.
(3) When comparing magnitude, force 6 > force 4 > force 3.
A. (1) and (2) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)

http://i617.photobucket.com/albums/tt257/michaelcoco_/21fc6c63.jpg

※試列明各點對與錯之原因※

回答 (1)

天同

2010-04-03 8:57 am

✔ 最佳答案

1. Statement (1) is wrong.
Average velocity = displacement/time. At t = x, the displacement of A, given by the area under the solid line, is larger than the area of B, as given by the area under the dotted line. Because of different displacements, their average velocities are different.

Statement (2) is correct.
Average acceleration = (final velocity - initial velocity)/time taken
Both have zero initial velocity, and the final velocities (i.e. velocity at t=x) are the same. Hence, both have the same average acceleration.

Statement (3) is correct.
By comparing the area under the solid line, which represents the distance travelled by A, with that under the dotted line, which represents the distance travelled by B. It can be seen that at any instant of time, the area under the solid line is always greater than that under the dotted line. Thus, the distance travelled by A is always greater than the distance travelled by B.

2. Statement (1) is correct.
In a free body diagram, only external forces are included. That is, only those forces given by an agent outside the system.
Forces 1 and 4 are both given by the earth (an external agent), whereas force 5 is given by the floor (also an external agent). Hence, they are all external forces.

Statement (2) is correct.
This is clear. Force 2 is the force given by mass m and acts on mass M. Force 3 is given by mass M and acts on mass m. They form a pair of action-reaction forces.

Statement (3) is correct.
Force 6 = (M+m)g , where g is the acceleration due to gravity
Force 4 = Mg, and Force 3 = mg
Clearly, Force 6 > Force 4 > Force 3

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