Physics Exam33,34

2007-01-05 11:32 pm

The ratio of the final kinetic energy to the initial kinetic energy of an object is one half. If the initial velocity of the object is 10 m/s, what is the final velocity?
a. 20 m/s b. 20 m/s squared c. 7.1 m/s d. 7.1 m/s squared
A mass is oscillating on a spring with a period of 4.60 s. At t = 0 s the mass has zero speed and is at x = 8.30 cm. What is the value of t the first time after t = 0 s that the mass is at x = 4.15 cm? a. 0.575 s b. 0.767 s c. 1.15 s d. 1.53 s

回答 (1)

myisland8132

2007-01-06 3:10 am

✔ 最佳答案

33
THE initial kinetic energy of an object =1/2m*100=50m
THE final kinetic energy of an object =1/2m*v^2=25m
v=squareroot(50)=7.1 m/s
ANSWER: C
34
The displacement is given by the function

圖片參考：http://upload.wikimedia.org/math/7/a/c/7ac3484c2b42686da65e26d84c792894.png

We then differentiate once to get an expression for the velocity at any time.

圖片參考：http://upload.wikimedia.org/math/f/c/d/fcd0e5911ca23e8d4642647d8106d340.png

And once again to get the acceleration at a given time.
Here
A=8.3
f=1/T=0.2174 Hz
v(0)=0
gamma=pi/2
that is
x(t)=8.3sin(2*pi*0.2174*t+pi/2)
=8.3sin(1.3653t+pi/2)
let x(t)=4.15
8.3sin(1.3653t+pi/2)=4.15
sin(1.3653t+pi/2)=0.5
1.3653t+pi/2=5pi/6
t=0.767s
The answer is B

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