Understanding Work and Gravity
* Work: Work is done when a force causes an object to move a certain distance. It's calculated as:
* Work (W) = Force (F) × Distance (d) × cos(θ)
* θ is the angle between the force and the direction of motion.
* Gravity: The Earth's gravitational force pulls objects towards its center. This force is always downward.
Scenarios
Let's consider the different directions the ball could move:
1. Straight Upward:
* The gravitational force (F) is downward, and the displacement (d) is upward. The angle between them is 180 degrees.
* Work = F × d × cos(180°) = - Fd (since cos(180°) = -1)
* The work done by gravity is negative, meaning gravity does negative work. This is because gravity acts against the upward motion of the ball.
2. Straight Downward:
* The gravitational force (F) is downward, and the displacement (d) is also downward. The angle between them is 0 degrees.
* Work = F × d × cos(0°) = Fd (since cos(0°) = 1)
* The work done by gravity is positive, meaning gravity does positive work. This is because gravity acts in the same direction as the ball's motion.
3. Horizontally:
* The gravitational force (F) is downward, and the displacement (d) is horizontal. The angle between them is 90 degrees.
* Work = F × d × cos(90°) = 0 (since cos(90°) = 0)
* No work is done by gravity because the force acts perpendicular to the direction of motion.
Calculating the Work
To get the specific values, we need to know the gravitational force acting on the ball. We can calculate that using:
* Force (F) = mass (m) × acceleration due to gravity (g)
* g = 9.8 m/s² (approximately)
Let's plug in the values for the upward and downward scenarios:
* F = 3 kg × 9.8 m/s² = 29.4 N
* Upward:
* Work = -Fd = - (29.4 N) × 2 m = -58.8 J
* Downward:
* Work = Fd = (29.4 N) × 2 m = 58.8 J
Summary
* Upward: Work done by gravity is -58.8 J (negative work).
* Downward: Work done by gravity is 58.8 J (positive work).
* Horizontally: Work done by gravity is 0 J (no work).
