多題mc (phy (force)+少許maths)

choice

Assume the gravitational acceleration g on the Earth to be 10 ms^-2


1. A ball on the ground is thrown upward with an initial speed of 20 ms^-1. Which
statement(s) is (are) correct?
I. The highest point that the ball can reach is 40 m above the ground.
II. Its speed will always decrease.
III. When the ball is 7.2 m above the ground, its speed is 16 ms^-1.
IV. The time for the ball to reach the highest point is 2 s.
A. I, IV
B. II, III.
C. III, IV.
D. II, III, IV.



2. A moving cart of 40 kg stops after sliding for 5 s on a rough road. The friction
acting on it is 400 N. Find its initial speed.
A. 5 ms^-1
B. 25 ms^-1
C. 50 ms^-1
D. 250 ms^-1



3. A block of 4 kg placed on a smooth plane of inclination 30°is connected with another of 1 kg bya massless string and a smooth pulley as shown in the figure below. Find the tension in the string and the acceleration of the blocks.
A. 8 N, 2 ms^-2.
B. 12 N, 2 ms^-2.
C. 10.93 N, 4.93 ms^-2.
D. 14.93 N, 4.93 ms^-2.

                               
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4. A ball of 0.1 kg hits vertically on the ground and bounces back. The ball and the ground
contact for 0.01 s. The speeds before and after the contact are both equal to 2 ms^-1. Find theaverage force acting on the ball by the ground.
A. 20 N
B. 39 N
C. 40 N
D. 41 N



5. A box is placed on a slope of inclination. The maximum magnitude of the friction acting on the
box by the slope is half of that of the normal force acting on the box by the slope. What is themaximum value of allowed such that the box will not slide down?
A.0.46°. B. 26.6°. C. 30°.D. 60°.



6. What is the probability of choosing a card from a deck and the card is an even number or a redcard or an ace?
A. 5/13
B. 1/2
C. 9/13
D. 19/26

                               
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小弟physics很渣,另外解答時請列出步驟,謝.

inthomaspy

Question 1
Statement 1 - False
By v^2 - u^2 = 2as
    0^2 - 20^2 = 2*-10*s
    s = 20m
Statement 2 - False
During the upward motion, the speed of the ball will gradually decrease from 20 ms^-1 to 0 ms^-1
but when the ball falls down, its speed will increase from 0 ms^-1
NB: speed =/= velocity
Statement 3 - True
By v^2 - u^2 = 2as
    LHS = 16^2 - 20^2 = -144
    RHS = 2*-10*7.2 = -144
Statement 4 - True
By v = u + at
    0 = 20 + -10*t
    t = 2s

Question 3
The technique of dealing with such type of question is to draw the free body diagram in horizontal plane
              4*10*sin30  <---  4kg mass --->  tension             tension <--- 1kg mass --->  1*10
                mgsin30                                    T                       T                                    mg
By Fnet = ma,
    T - 4*10*sin30 = 4a   ...(1)
    1*10 - T = 1a               ...(2)
solving (1) & (2), T = 12, a = -2

Question 4
Take downward direction be positive
before impact, u = + 2ms^-1        <<< the motion of the ball is vertically downward
after impact, v = - 2ms^-1        <<< the motion of the ball is vertically upward
By Ft = mv - mu,
average force acted on the ball = F = (mv - mu) / t = (0.1*-2 - 0.1*+2) / 0.01 = -40
the negative sign means when the ball hits the ground, there exist a force acted by the ground on the ball vertically upward

Question 6
In a deck, there are number 2, 4, 6, 8, 10 which are even
Hence there are 5 * 4 (number of even numbers * number of cards for each number) cards  = 20 cards for even
There are 26 cards which are red, but excluding the red cards for even numbers
There are 16 cards for red which are not even numbers
Finally, there are 4 cards for ace, but 2 cards of ace are red
Hence 2 cards for ace which are not red

Required probability
= [20(even) + 16(red excluding 'even red' as the 'even red' are counted before) + 2(ace excluding red)] / 52

Question 8
代數問題...
I = 10^-4, Io = 10^-12
B = 10 log (10^-4 / 10^-12) = 80
also...answer A, B, D seems not practical...
A is too large...B is too small...D is too small too (we seldom hear sound of negative sound intensity level)...