91Ó°ÊÓ

Understanding the gravitational force acting on an object is crucial in solving problems related to motion, especially in circular paths. The gravitational force can be calculated using the formula:\[ F = m \times g \]where:

• \( F \) is the gravitational force,
• \( m \) is the mass of the object, and
• \( g \) is the acceleration due to gravity, approximately \(9.8 \, m/s^2\) on Earth.

For instance, if you have a mass \( m = 2 \, kg \), you can easily find the gravitational force by multiplying the mass and gravity: \( F = 2 \, kg \times 9.8 \, m/s^2 = 19.6 \, N \). This simple yet essential calculation tells us how much force the Earth exerts on the object. To advance further into solving problems involving vertical circular motion, this force forms the basis of calculating other necessary parameters like work done.

Displacement in the context of vertical circular motion refers to the straight-line distance between two points in the path of motion. When an object moves from the lowest point of a circle to the highest point, it's crucial to consider the diameter of the circle for calculating displacement. Since the radius is the distance from the center to the perimeter, the total vertical displacement from bottom to top is twice the radius.In this problem, the radius of our vertical circle is given as \(2 \, m\). Hence, the displacement, defined as the direct upwards path from the lowest to the highest point, is \(2 \times 2 \, m = 4 \, m\). The displacement here captures the actual vertical movement, not the path travelled along the curved circle. This displacement is vital for determining the work done by forces in play during this motion, as it provides the necessary direction and magnitude element for our calculations.

In physics, the work done by a force is a measure of energy transfer and is calculated when a force moves an object through a distance. It can be computed using the formula:\[ W = F \times d \]where:

• \( W \) is the work done,
• \( F \) is the force in the same direction as displacement, and
• \( d \) is the displacement the force acts upon.

In the scenario of vertical circular motion, when moving from the lowest point to the highest point, work is done against gravitational force. Using our calculated values:

• \( F = 19.6 \, N \)
• \( d = 4 \, m \)

Plugging these into the formula, we get \( W = 19.6 \, N \times 4 \, m = 78.4 \, J \). This result represents the energy expended by the gravitational force over the given displacement in the circle. Understanding how to apply the work done formula helps in analyzing the energy changes in systems involving forces and motion.