A clock has an aluminum pendulum with a period of 1.000 s at 20.3 °C. Suppose the clock is moved to a location where the average temperature is 28.1 °C. (The linear expansion coefficient for aluminum is 2.20 10-5 °C−1.)
(a) Determine the new period of the clock's pendulum. (Enter your answer to six siginficant figures.)
(b)Determine how much time the clock will lose in 2 weeks.
There are two standard equations here: what is it you have a question about?
what equations do i use?
a.
Moment of inertia respectively the axis
that passes through the end of the pendulum is
I = Io+mx^2 = mL^2/12 + mL^2/4 = mL^2/3.
T1 = sqrt(I/m•g•x) = sqrt( mL^2/3m•g•x)
=sqrt( L^2/3•g•x) = L/sqrt(3•g•x) =1 s.
L = sqrt(3•g•x),
α =ΔL/(L•ΔT),
ΔL = α •sqrt(3•g•x) • ΔT,
T2 = sqrt ((L+ ΔL)^2/3•g•x) =
=(L+ΔL)/ sqrt(3•g•x)=
= (L + α •sqrt(3•g•x) • ΔT)/ sqrt(3•g•x) =
= ( sqrt(3•g•x) + α •sqrt(3•g•x) • ΔT)/ sqrt(3•g•x)=
= 1+7.8•2.2•10^-5 = 1.000172 s.
b.
Δto= 0.000172 s.
Δt =0.000172•3600•24•14 = 208.0512 s.
can you help more, i didn't get the right answer..i didn't get where you got 7.8 from
ΔT = 28.1 -20.3 = 7.8 oC
i didn't get the right answer
What is the right answer?
Why do you believe that this answer is incorrect?
i get it wring when i enter it
To determine the new period of the clock's pendulum, we can use the equation:
T2 = T1 * sqrt(L2 / L1),
where T2 is the new period, T1 is the original period, L2 is the new length, and L1 is the original length.
Since the material of the pendulum is aluminum, we need to consider the expansion due to the change in temperature. The length change can be calculated using:
ΔL = α * L1 * ΔT,
where ΔL is the change in length, α is the linear expansion coefficient for aluminum, L1 is the original length of the pendulum, and ΔT is the change in temperature.
Given:
T1 = 1.000 s,
ΔT = 28.1 °C - 20.3 °C = 7.8 °C,
α = 2.20 x 10^(-5) °C^(-1).
(a) To find the new period:
1. Calculate the change in length:
ΔL = α * L1 * ΔT
= (2.20 x 10^(-5) °C^(-1)) * L1 * (7.8 °C).
2. Calculate the new length:
L2 = L1 + ΔL.
3. Calculate the new period:
T2 = T1 * sqrt(L2 / L1).
(b) To determine how much time the clock will lose in 2 weeks:
1. Calculate the number of seconds in 2 weeks:
Number of seconds in 2 weeks = 2 weeks * 7 days/week * 24 hours/day * 60 minutes/hour * 60 seconds/minute.
2. Find the number of periods in 2 weeks:
Number of periods = Number of seconds in 2 weeks / T1.
3. Calculate the lost time:
Lost time = Number of periods * (T1 - T2).
Now, let's calculate the new period and how much time the clock will lose in 2 weeks.