Answer: The mass of the sculpture is 11.8kg
Explanation:
Using the equation of fundamental frequency of a taut string.
f = (1/2L)*√(T/μ) .... (Eqn1)
Where
f= frequency in Hertz =80Hz
T = Tension in the string = Mg
M represent the mass of the substance (sculpture) =?
g= 9.8m/s^2
L= Length of the string=90cm=0.9m
μ= mass density = mass of string /Length of string
mass of string =5g=0.005kg
L=0.9m
μ=0.005/0.9 = 0.0056kg/m
Using (Eqn1)
80= 1/(2*0.9) √(T/0.0056)
144= √(T/0.0056)
Square both sides
20736= T/0.0056
T= 116.12N
Recall that T =Mg
116.12= M * 9.8
M=116.12/9.8
M= 11.8kg
Therefore the mass of the sculpture is 11.8kg
Answer:
a. 0.275m/s
b. 1.08m
Explanation:
Since the duck the paddle the water at an interval of 1.6sec, we can determine the frequency of the wave formed using the equation
f=1/T
Where T is the period.
f=1/1.6
f=0.625Hz.
Also from the equation used in determining the speed of a wave
V=fλ,
v=0.625*0.2
v=0.125m/s
in the question it was stated that that the duck produce a wave moving at a speed of 0.40m/s.
Hence the speed of the duck is
v(duck)=0.40-0.125
v(duck)=0.275m/s
b. The distance between the crest behind the duck is the wavelength of the waves.
To determine this, the wavelength is expressed as
λ=v/f
but the speed in this case is the speed of the duck and the surface wave,as this account for the wave speed behind the duck,
Hence we have
λ=(0.40+0.275)/0.625
λ=1.08m.
The wavelength behind the duck is 1.08m
Kinematic question!
Start with your knowns!

we want to find x!
the only kineamtic that works with this info is the third!

so we plug in our values and get

this'll equal out to -159.2 meters.
our units equal out, so we know our answer is correct!
Answer:
=8.0 Watts
Explanation:
Power is a ratio of work done over time. The power in an electric circuit is calculated using the following formula:
P=I²R
P is power, I is current, R is resistance
Therefore, Power= 4²ₓ 0.5Ω
=8.0 Watts
Answer:
4276.98 years
Explanation:
t = age of the sample in numbers of years
T = half life of the carbon-14 isotope = 5730 yrs
λ = decay constant of carbon-14
decay constant is given as



A₀ = activity of Carbon-14 in living plants
A = activity of Carbon-14 after time "t" = (0.596) A₀
Using the equation



t = 4276.98 years