"Determine the restoring force of a pendulum that is pulled to an angle of 12.0 degrees left of the vertical. The mass of the bob is 300.0g."
To determine the restoring force of a pendulum, you need to use the concept of gravitational force and the given angle of displacement. Here are the steps to find the restoring force:
1. Convert the mass of the bob to kilograms:
- Given: mass = 300.0g
- Convert grams to kilograms: 300.0g ÷ 1000 = 0.300kg
2. Determine the gravitational force acting on the pendulum bob:
- The gravitational force is given by the formula: F = m × g
- Where F is the force, m is the mass, and g is the acceleration due to gravity.
- The value of g is approximately 9.81 m/s^2.
- Calculate: F = 0.300kg × 9.81 m/s^2 = 2.943 N
3. Find the horizontal component of the gravitational force:
- The restoring force acts perpendicular to the displacement of the pendulum bob.
- Since the pendulum is pulled to an angle of 12.0 degrees left of the vertical, the restoring force will have a horizontal component.
- Calculate: F_horizontal = F × sin(θ)
- Where θ is the angle of displacement.
- Convert the angle of displacement from degrees to radians: θ = 12.0° × π/180
- Calculate: F_horizontal = 2.943 N × sin(12.0° × π/180) ≈ 0.611 N
Therefore, the restoring force of the pendulum when pulled to an angle of 12.0 degrees left of the vertical is approximately 0.611 N.