To find the mass of the body, we can start by using Newton's second law of motion, which states that the acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.
Let's break down the given information:
- Magnitude of the first force: F1
- Magnitude of the second force: F2
- Angle between the two forces: θ
- Magnitude of the resulting acceleration: a
- Mass of the body: ?
Now, we need to analyze the forces acting on the body. Since there are only two forces, F1 and F2, the resulting force can be found using vector addition. We can use the parallelogram law of vector addition or decompose the forces into their x and y components.
Let's decompose the forces into their x and y components:
- F1x = F1 * cos(θ)
- F1y = F1 * sin(θ)
- F2x = F2 * cos(0) = F2
- F2y = F2 * sin(0) = 0
Since the forces are acting in different directions, we need to find the net force by adding their x and y components:
- Fx = F1x + F2x = F1 * cos(θ) + F2
- Fy = F1y + F2y = F1 * sin(θ) + 0 = F1 * sin(θ)
Now, we can find the magnitude of the net force using the Pythagorean theorem:
- F = √(Fx² + Fy²) = √((F1 * cos(θ) + F2)² + (F1 * sin(θ))²)
We know that the net force is related to the mass and acceleration of the body through the equation:
- F = m * a
Substituting the magnitude of the net force calculated above, we get:
- √((F1 * cos(θ) + F2)² + (F1 * sin(θ))²) = m * a
Finally, we solve for the mass:
- m = √((F1 * cos(θ) + F2)² + (F1 * sin(θ))²) / a
By substituting the given values for F1, F2, θ, and a into the equation, we can calculate the mass of the body.