The block of mass 3.43553 kg has an acceleration

of 2.1 m/s^2 as shown.

/
/ F
a _____________ <-/ )23 degree
<---- |_3.43553kg_|

What is the magnitude of F? Assume the acceleration due to gravity is 9.8 m/s^2 and the surface is frictionless.

Answer in units of N

To find the magnitude of force (F), we need to consider the forces acting on the block: the force due to gravity (mg) and the force causing the acceleration (F). We can resolve the forces into components parallel and perpendicular to the inclined plane.

First, let's find the force exerted by gravity (mg) perpendicular to the inclined plane. The force perpendicular to the inclined plane is mg * cos(theta), where theta is the angle of the incline. Given that the mass (m) is 3.43553 kg and the acceleration due to gravity (g) is 9.8 m/s^2, the force perpendicular to the inclined plane is:

Force perpendicular = 3.43553 kg * 9.8 m/s^2 * cos(23 degrees) = 30.684 N

Next, let's find the force exerted by gravity (mg) parallel to the inclined plane. The force parallel to the inclined plane is mg * sin(theta). Using the same values as before, the force parallel to the inclined plane is:

Force parallel = 3.43553 kg * 9.8 m/s^2 * sin(23 degrees) = 15.816 N

Since the surface is frictionless, the only force causing the acceleration on the block is F. Therefore, F is equal to the force parallel to the inclined plane, which is:

F = 15.816 N

So, the magnitude of force (F) is 15.816 N.

To find the magnitude of force F, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the mass of the block is given as 3.43553 kg, and the acceleration is given as 2.1 m/s^2. However, we need to resolve the acceleration into two components: one parallel to the incline and one perpendicular to it.

The parallel component of the acceleration can be found by multiplying the total acceleration (2.1 m/s^2) by the cosine of the angle of inclination (23 degrees):

a_parallel = 2.1 m/s^2 * cos(23 degrees)
a_parallel = 2.1 m/s^2 * 0.9205
a_parallel ≈ 1.9321 m/s^2

The perpendicular component of the acceleration can be found by multiplying the total acceleration (2.1 m/s^2) by the sine of the angle of inclination (23 degrees):

a_perpendicular = 2.1 m/s^2 * sin(23 degrees)
a_perpendicular = 2.1 m/s^2 * 0.3894
a_perpendicular ≈ 0.8174 m/s^2

Since the surface is frictionless, the force F is the only force acting on the block. The magnitude of F can be found by using the formula F = m * a, where m is the mass of the block and a is the parallel component of the acceleration:

F = 3.43553 kg * 1.9321 m/s^2
F ≈ 6.265 N

Therefore, the magnitude of force F is approximately 6.265 N.

F = M*a.