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?

b.) What is the horizontal speed of the block 4.50 seconds after it starts moving?
c.) What is the magnitude of the normal force acting on the block when the force F is acting on it?
d.) If, instead, the floor has a coefficient of kinetic friction µk = 0.04, what is the magnitude of the frictional force on the block when the block is moving?

a. a=Fn/m=11.8*cos23 / 3.24=3.35 m/s^2.

b. V = Vo + at,
V = 0 + 3.35*4.5 = 15.75 m/s.

c. Fv = mg -F*sin23,
Fv = 3.24*9.8 - 11.8sin23 = 27.1 N.

d. Fk = u*Fv = 0.04 * 27.1 = 1.09 N.

To solve these problems, we can break down the force into its horizontal and vertical components.

a) Magnitude of acceleration (a):

Using Newton's second law, the net force acting on the block is equal to its mass multiplied by its acceleration:

ΣF = ma

Since the force is applied at an angle above the horizontal, we need to find the horizontal component of the force:

F_horizontal = F * cos(theta)

The net force can be calculated as:

ΣF = F_horizontal = ma

Substituting the given values:

11.8N * cos(23.0 degrees) = 3.24 kg * a

Simplifying:

a = (11.8N * cos(23.0 degrees)) / 3.24 kg

a ≈ 3.42 m/s²

Therefore, the magnitude of the acceleration of the block is approximately 3.42 m/s².

b) Horizontal speed after 4.50 seconds:

To find the horizontal speed of the block after 4.50 seconds, we can use the equation:

v = v₀ + at

Where:
v is the final velocity (horizontal speed),
v₀ is the initial velocity (0 m/s in this case),
a is the acceleration (from part a), and
t is the time (4.50 seconds).

Plugging in the values:

v = 0 + (3.42 m/s²) * (4.50 s)

v ≈ 15.39 m/s

Therefore, the horizontal speed of the block after 4.50 seconds is approximately 15.39 m/s.

c) Magnitude of the normal force:

The normal force is the force exerted by a surface to support the weight of an object resting on it). In this case, the block is on a horizontal frictionless floor, so the normal force will be equal to the block's weight:

Normal force (N) = weight (mg)

Finding the weight:

Weight (mg) = mass (m) * acceleration due to gravity (g)

Weight = 3.24 kg * 9.8 m/s²

Weight ≈ 31.75 N

Therefore, the magnitude of the normal force acting on the block when the force F is acting on it is approximately 31.75 N.

d) Magnitude of the frictional force:

To find the magnitude of the frictional force on the block when it is moving with a coefficient of kinetic friction (µk) of 0.04, we can use the equation:

Frictional force (f) = µk * N

Substituting the given values:

f = 0.04 * 31.75 N

f ≈ 1.27 N

Therefore, the magnitude of the frictional force on the block when it is moving is approximately 1.27 N.

To solve this problem, we can break down the given information and apply Newton's laws of motion. Let's go through each part:

a) To find the magnitude of the acceleration of the block when the force is applied, we need to use Newton's Second Law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).

In this case, the force F is given as 11.8N, and the mass of the block is 3.24 kg. However, the force is acting at an angle theta of 23.0 degrees above the horizontal. To find the acceleration, we need to convert the force into its horizontal and vertical components.

The horizontal component of the force can be calculated using the formula F_horizontal = F * cos(theta), where F is the magnitude of the force and theta is the angle above the horizontal. Substituting the given values, we have F_horizontal = 11.8N * cos(23.0 degrees).

The vertical component of the force can be calculated using the formula F_vertical = F * sin(theta), where F is the magnitude of the force and theta is the angle above the horizontal. Substituting the given values, we have F_vertical = 11.8N * sin(23.0 degrees).

Since there is no friction and the floor is frictionless, the horizontal component of the force is the only force responsible for accelerating the block horizontally. We can equate this force to the mass of the block multiplied by its acceleration (F_horizontal = m * a).

Solving for the acceleration (a), we have a = F_horizontal / m. Substitute the calculated value of F_horizontal and the given mass of the block to find the magnitude of the acceleration.

b) To find the horizontal speed of the block 4.50 seconds after it starts moving, we can use the kinematic equation: v = v0 + at, where v is the final velocity (horizontal speed), v0 is the initial velocity (which is zero since the block starts from rest), a is the acceleration (which can be found from part a), and t is the time (4.50 seconds).

Substitute the values into the equation to find the horizontal speed of the block after 4.50 seconds.

c) To find the magnitude of the normal force acting on the block when the force F is acting on it, we need to consider the forces acting on the block in the vertical direction. Since the block is on a horizontal frictionless floor and there is no vertical acceleration, the normal force from the floor balances the vertical component of the force acting on the block (F_vertical).

The magnitude of the normal force is the same as the magnitude of the force acting downwards on the block, which is the weight of the block. The weight can be calculated using the formula weight (W) = mass (m) * gravitational acceleration (g). Substitute the given mass of the block and the value of gravitational acceleration to find the magnitude of the normal force.

d) If the floor has a coefficient of kinetic friction (µk) = 0.04, the frictional force on the block when it is moving can be found using the formula frictional force (F_friction) = µk * normal force (F_normal). The normal force can be found from part c. Substitute the given coefficient of kinetic friction and the magnitude of the normal force to find the magnitude of the frictional force.

By following these steps and calculations, you will be able to find the answers to all the parts of the question.