Question

Mathematically solve for the Force applies to hold a pendulum bob stationary 0.15 m away from the vertical axis as it’s being held by a 4.0 m string attached to a ledge

Answer 1

To mathematically solve for the force applied to hold a pendulum bob stationary, we can use the equilibrium condition at the bob's maximum displacement.

The force applied to hold the bob stationary is equal to the tension in the string.

Let's assume the angle made by the string with the vertical axis is θ.

From the right triangle formed by the string, ledge, and vertical axis, we have:

sin(θ) = 0.15 m / 4.0 m

Simplifying,

sin(θ) = 0.0375

Now, to solve for the force applied, we can use the equilibrium condition:

Tension = mg cos(θ)

where Tension is the force applied, m is the mass of the bob, and g is the acceleration due to gravity.

Assuming we know the mass of the bob, let's say m = 1 kg, and the acceleration due to gravity is g = 9.8 m/s^2, we can plug in the values:

Tension = 1 kg * 9.8 m/s^2 * cos(arcsin(0.0375))

Using a calculator, we can calculate the value inside the cos function:

θ ≈ arcsin(0.0375) ≈ 2.15°

Now, substituting this value back into the tension equation:

Tension ≈ 1 kg * 9.8 m/s^2 * cos(2.15°)

Using a calculator, we can evaluate the expression:

Tension ≈ 9.79 N

Therefore, the force applied to hold the pendulum bob stationary is approximately 9.79 Newtons.