The only two forces acting on a body have magnitudes F1 and F2 and directions that differ by an angle θ. If the resulting acceleration has a magnitude a, what is the mass of the body?

Fx = F1 + F2 cos T

Fy = F2 sin T

F = sqrt (Fx^2+Fy^2)

Fx^2 = F1^2 + 2 F1F2 cos T + F2^2 cos^2 T
Fy^2 = F2^2 sin^2 T

sum = F1^2 + 2 F1F2 cos T + F2^2(sin^2T+cos^2T)

sum = F1^2 + 2 F1 F2 cos T + F2^2
so
F = sqrt (F1^2 + 2 F1 F2 cos T + F2^2)
and
m = F/a
=(1/a)sqrt(F1^2 + 2 F1 F2 cos T + F2^2)

To find the mass of the body, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

Let's consider the forces F1 and F2. Since they have magnitudes F1 and F2 and directions that differ by an angle θ, we can break them down into their respective components along the direction of acceleration.

The component of F1 along the direction of acceleration is F1 * cos(θ), and the component of F2 along the direction of acceleration is F2 * cos(θ).

The net force acting on the body is the sum of these components:

Net force = F1 * cos(θ) + F2 * cos(θ)

According to Newton's second law, the net force is equal to the product of the mass (m) of the body and its acceleration (a):

m * a = F1 * cos(θ) + F2 * cos(θ)

Now, we can solve this equation for the mass (m):

m = (F1 * cos(θ) + F2 * cos(θ)) / a

Therefore, the mass of the body can be calculated by dividing the sum of the magnitudes of the components of the forces along the direction of acceleration (F1 * cos(θ) + F2 * cos(θ)) by the magnitude of the resulting acceleration (a).

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.