Answer:
a) f=0.1 Hz ; b) T=10s
c)λ= 36m
d)v=3.6m/s
e)amplitude, cannot be determined
Explanation:
Complete question is:
Determine, if possible, the wave's (a) frequency, (b) period, (c) wavelength, (d) speed, and (e) amplitude.
Given:
number of wave crests 'n'= 5
pass in a time't' 54.0s
distance between two successive crests 'd'= 36m
a) Frequency of the waves 'f' can be determined by dividing number of wave crests with time, so we have
f=n/t
f= 5/ 54 => 0.1Hz
b)The time period of wave 'T' is the reciprocal of the frequency
therefore,
T=1/f
T=1/0.1
T=10 sec.
c)wavelength'λ' is the distance between two successive crests i.e 36m
Therefore, λ= 36m
d) speed of the wave 'v' can be determined by the product of frequency and wavelength
v= fλ => 0.1 x 36
v=3.6m/s
e) For amplitude, no data is given in this question. So, it cannot be determined.
Answer:
A) a = 73.304 rad/s²
B) Δθ = 3665.2 rad
Explanation:
A) From Newton's first equation of motion, we can say that;
a = (ω - ω_o)/t. We are given that the centrifuge spins at a maximum rate of 7000rpm.
Let's convert to rad/s = 7000 × 2π/60 = 733.04 rad/s
Thus change in angular velocity = (ω - ω_o) = 733.04 - 0 = 733.04 rad/s
We are given; t = 10 s
Thus;
a = 733.04/10
a = 73.304 rad/s²
B) From Newton's third equation of motion, we can say that;
ω² = ω_o² + 2aΔθ
Where Δθ is angular displacement
Making Δθ the subject;
Δθ = (ω² - ω_o²)/2a
At this point, ω = 0 rad/s while ω_o = 733.04 rad/s
Thus;
Δθ = (0² - 733.04²)/(2 × 73.304)
Δθ = -537347.6416/146.608
Δθ = - 3665.2 rad
We will take the absolute value.
Thus, Δθ = 3665.2 rad
