A simple pendulum consists of a ball connected to one end of a thin brass wire. The period of the pendulum is 2.15 s. The temperature rises by 133 C°, and the length of the wire increases. Determine the change in the period of the heated pendulum.

T=2πsqrt(L/g) => L=T²g/4π²=

=2.15²•9.8/4•π²=1.1475 m
L₁=L+ΔL = L+αLΔt=
=1.1475 + 19•10⁻⁶•1.1475•133 =1.1504 m
T₁=2 πsqrt(L₁/g) =
= 2 πsqrt(1.1504/9.8)=2.1527 s
ΔT =2.1527-2.15=0.0027 s

Well, when the temperature rises by 133 degrees, that's definitely heating things up! Now, in terms of the change in the period of the pendulum, let's see what effect that has.

In this case, the length of the wire increases due to the temperature rise. If the length of the wire increases, it means the distance traveled by the ball will also increase. And when distance increases, we can expect the period of the pendulum to also increase. So, the change in the period of the heated pendulum would be... drumroll, please... longer! It will be longer than the period before the temperature rise.

To determine the change in the period of the heated pendulum, you need to consider the effect of temperature on the length of the wire and the relationship between the period and the length of the pendulum.

Here are the steps to calculate the change in the period:

1. Determine the change in length caused by the temperature increase:
- Find the coefficient of linear expansion for brass.
- Multiply the original length of the wire by the coefficient of linear expansion and the change in temperature to get the change in length.

2. Calculate the new length of the wire:
- Add the change in length to the original length of the wire.

3. Calculate the change in the period:
- Use the formula for the period of a simple pendulum: T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
- Calculate the original period using the original length of the wire.
- Calculate the new period using the new length of the wire.
- Subtract the original period from the new period to get the change in the period.

Let's go through these steps in detail.

Step 1: Determine the change in length caused by the temperature increase.

To find the coefficient of linear expansion for brass:
- Look up the coefficient of linear expansion for brass or assume it as 19 x 10^(-6) C^(-1) for an approximate value.

Let's assume the original length of the wire as L and the change in temperature as ΔT.
The change in length of the wire can be calculated as:
ΔL = (19 x 10^(-6) C^(-1)) × L × ΔT

Step 2: Calculate the new length of the wire.

The new length of the wire will be the sum of the original length and the change in length:
New length = L + ΔL

Step 3: Calculate the change in the period.

Use the formula for the period of a simple pendulum:
T = 2π√(L/g)

Let's assume the acceleration due to gravity (g) as 9.8 m/s^2 for simplicity.

Calculate the original period:
Original period (T1) = 2π√(L/g)

Calculate the new period:
New period (T2) = 2π√(New length/g)

Calculate the change in period:
Change in period = T2 - T1

By following these steps, you can determine the change in the period of the heated pendulum.

To determine the change in the period of a heated pendulum, we need to consider how the length of the wire changes with temperature. The formula for the period of a pendulum is given by:

T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

We know the initial period of the pendulum (2.15 s), but we need to determine the change in the length of the wire due to the increase in temperature. To do this, we can use the coefficient of linear expansion for brass. Let's assume the initial length of the wire is L and the change in temperature is ΔT.

The change in length of the wire is given by:

ΔL = αLΔT

where α is the coefficient of linear expansion for brass.

We can substitute the equation for the change in length into the formula for the period:

T' = 2π√((L + ΔL)/g)

Now, we can substitute the expression for ΔL we found earlier:

T' = 2π√((L + αLΔT)/g)

Next, we can factor out L:

T' = 2π√(L(1 + αΔT)/g)

Finally, we can simplify the equation:

T' = √(1 + αΔT) * T

where T' is the new period of the pendulum.

To determine the change in the period, we can subtract the initial period from the new period:

ΔT = T' - T = √(1 + αΔT) * T - T

Now we have a formula to calculate the change in the period of the pendulum given the change in temperature and the initial period.