Question

a grandfather clock ticks each time the pendulum passes through the lowest point. if the pendulum is modeled as a sim- ple pendulum, how long must it be for the ticks to occur once a second?

Answer 1

To make the pendulum tick once a second, its length should be approximately 0.249 meters.

Step-by-step explanation:

In order for the grandfather clock to tick once a second, the length of the pendulum must be adjusted to match the desired frequency. The period of a simple pendulum is given by the equation T = 2pi*sqrt(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. To find the length of the pendulum needed for a period of 1 second, we can rearrange the equation as L = (T^2*G)/(4pi^2), where G is the acceleration due to gravity.

Let's substitute the values into the equation:

L = (1^2*9.8)/(4*3.14^2) = (9.8)/(4*9.87) = 0.249 m

So, the length of the pendulum must be approximately 0.249 meters for the ticks to occur once a second.

Answer 2

The pendulum must have a length of approximately 0.248 meters (or 24.8 centimeters) for the ticks to occur once a second.

The time it takes for the ticks of a grandfather clock to occur once a second depends on the length of the pendulum. To determine the length needed for the ticks to occur once a second, we can use the formula for the period of a simple pendulum.

The period, T, of a simple pendulum is given by the equation:

T = 2π√(L/g),

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

To find the length of the pendulum needed for the ticks to occur once a second, we can rearrange the equation:

1 = 2π√(L/g).

Squaring both sides of the equation, we get:

1^2 = (2π)^2(L/g).

Simplifying, we have:

1 = 4π^2(L/g).

Now, we can solve for L by isolating it:

L = g/(4π^2).

Given that the acceleration due to gravity, g, is approximately 9.8 m/s^2, we can substitute this value into the equation:

L = 9.8/(4π^2).

Calculating this value, we find:

L ≈ 0.248 meters.