A simple pendulum consists of a ball connected to one end of a thin brass wire. The period of the pendulum is 1.45 s. The temperature rises by 142 C°, and the length of the wire increases. Determine the change in the period of the heated pendulum.

assuming you have zero calculus.

period=2PI sqrt (l/g)
solve for original length l.

now, change in length=l*coeffexpansion*dTemp
now compute change in length.

add that to the oiginal length, compute new period, then change in period.

If you have calculus, it is straigthforward.

To determine the change in the period of the heated pendulum, we can use the formula for the period of a simple pendulum:

T = 2π √(L / g)

Where:
T = period
L = length of the pendulum
g = acceleration due to gravity

In this case, we know the initial period (T_initial = 1.45 s) and we need to find the change in the period (∆T). We are also given that the temperature rises by 142°C (ΔT°) and that the length of the wire increases.

Let's break down the problem into steps:

Step 1: Convert the change in temperature from Celsius to Kelvin.
Since Celsius and Kelvin are on the same scale, we can simply add 273 to the change in temperature.
ΔT_K = ΔT°C + 273

Step 2: Calculate the change in the length of the wire.
The change in length (ΔL) of the wire can be calculated using the coefficient of linear expansion (α) and the initial length (L_initial) of the wire.
ΔL = α * L_initial * ΔT_K

Step 3: Calculate the new length (L_final) of the wire.
L_final = L_initial + ΔL

Step 4: Calculate the change in the period (∆T) of the heated pendulum.
∆T = T_final - T_initial

Step 5: Substitute the values into the formulas and calculate:
∆T_K = 142°C + 273 = 415 K

Let's assume the coefficient of linear expansion for brass is α = 19 x 10^(-6)/°C.
L_initial = L (length of the wire)
ΔL = (19 x 10^(-6)/°C) * L_initial * 142°C
L_final = L_initial + ΔL
∆T = 2π √(L_final / g) - 2π √(L_initial / g)

Please provide the initial length of the wire (L) and the acceleration due to gravity (g) to continue with the calculation.

To determine the change in the period of the heated pendulum, we need to 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.

Let's break down the problem step by step:

Step 1: Calculate the initial length of the pendulum wire.
Assuming the initial length of the wire is L0, we have the initial period T0 = 1.45 s. Rearranging the formula, we get:

L0 = (T0^2 * g) / (4π^2)

Step 2: Calculate the change in length of the wire due to the temperature increase.
Let's assume the change in length of the wire is ΔL. Since the length increases, our change in length will be positive. We can calculate it using the linear thermal expansion formula:

ΔL = α * L0 * ΔT

where α is the coefficient of linear expansion for brass, ΔT is the change in temperature, and L0 is the initial length of the wire.

Step 3: Calculate the new length of the wire after heating.
The new length of the wire can be calculated as:

L1 = L0 + ΔL

Step 4: Calculate the new period of the heated pendulum.
Using the formula for the period of a simple pendulum, we have:

T1 = 2π√(L1/g)

Step 5: Determine the change in the period.
The change in the period can be calculated as:

ΔT = T1 - T0

Now you can substitute the known values and calculate the change in the period of the heated pendulum. Make sure to use the correct units and physical constants in your calculations.