A 3.24 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a force F=11.8N at an angle theta=23.0degrees above the horizontal, as shown. What is the magnitude of the acceleration of the block when the force is applied?

Now I did that coffee cup. You do some.

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

First, we need to resolve the applied force into its horizontal and vertical components. The horizontal component of the force can be calculated as F_h = F * cos(theta), and the vertical component of the force can be calculated as F_v = F * sin(theta).

Given:
Mass of the block (m) = 3.24 kg
Applied force (F) = 11.8 N
Angle (theta) = 23.0 degrees

Calculating the horizontal component of the force:
F_h = F * cos(theta)
F_h = 11.8 N * cos(23.0 degrees)
F_h = 11.8 N * 0.9205
F_h ≈ 10.84 N

Since there is no friction and the floor is horizontal, the horizontal component of the force does not affect the object's motion. Thus, we can ignore it when calculating acceleration.

The vertical component of the force is responsible for the acceleration of the block. Therefore, we can write the net force equation using the vertical component of the force:

Net force (F_net) = m * a
F_v = m * a

Substituting the known values:
F_v = 3.24 kg * a
F_v = 3.24a

Solving for acceleration (a):
a = F_v / m
a = (11.8 N * sin(23.0 degrees)) / 3.24 kg
a ≈ (11.8 N * 0.3907) / 3.24 kg
a ≈ 1.426 m/s^2

Therefore, the magnitude of the acceleration of the block when the force is applied is approximately 1.426 m/s^2.

To determine the magnitude of the acceleration of the block when the force is applied, you can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.

In this case, the net force on the block is the force applied by the cord at an angle above the horizontal. We can break this force into its horizontal and vertical components. The horizontal component of the force will not result in any acceleration since there is no horizontal friction, so we only need to consider the vertical component of the force.

The vertical component of the force can be found using trigonometry. Given that the force F is 11.8 N at an angle theta of 23.0 degrees, the vertical component Fy can be calculated as:

Fy = F * sin(theta)

Substituting the given values:
Fy = 11.8 N * sin(23.0 degrees)

Now, we have the vertical component of the force applied to the block. We can use Newton's second law to calculate the acceleration.

a = F_net / m

Since the vertical component of the force is acting upwards, we can say that the net force in the vertical direction is equal to the force Fy. Therefore:

a = Fy / m = (11.8 N * sin(23.0 degrees)) / 3.24 kg

Evaluating this expression gives us the magnitude of the acceleration of the block when the force is applied.