A force F = (4.18xi + 3.18yj) N acts on an object as it moves in the x direction from the origin to x = 4.34 m. Calculate the work done on the object by the force.
Work= INTEGRAL f.dx= 4.18x^2/2 at limits
or 1/2 4.18(4.34^2) joules.
To calculate the work done on an object by a force, you can use the formula:
Work = Force * Displacement * cos(theta)
Where:
- Force is the vector representing the force applied to the object
- Displacement is the vector representing the displacement of the object
- Theta is the angle between the force vector and the displacement vector
Let's break down the given values and solve the problem step by step:
Given:
Force, F = (4.18xi + 3.18yj) N
Displacement, D = 4.34 m
Step 1: Calculate the angle between the force vector and displacement vector
Since the force is in the x-direction (along the positive x-axis) and the object is moving in the x-direction, the angle theta between the force and displacement vectors is 0 degrees (or 180 degrees, assuming a positive value).
Step 2: Calculate the work done
Using the formula, Work = Force * Displacement * cos(theta), we substitute the given values:
Work = (4.18xi + 3.18yj) N * 4.34 m * cos(0)
The cosine of 0 degrees is 1, so the equation simplifies to:
Work = (4.18 * 4.34) J
Calculating this:
Work = 18.1152 J
Therefore, the work done on the object by the force is approximately 18.12 Joules.