A 40N force applied at an angle of 37 degrees above the horizontal pulls a 5kg box on a horizontal floor. the acceleration of the box is 3meter per second square. how large a frictional force must be retarding the motion of the box.

a.50N b.13N c.17N d.25N

Wb = mg = 5kg * 9.8N/kg = 49 N.

Fb = 49N @ 0 Deg. = Force of box.
Fp = 49*sin(0) = 0. = Force parallel to
floor.
Fv = 49*cos(0) = 49 N. = Force perpendicular to floor.

Fv'=Fv-Fap*sin37 = 49-40sin37 = 24.9 N.
= Normal. = Net force perpendicular to
floor.

Fn = Fap*cosA-Fp-Fk = ma.
40*cos37-0-Fk = 5*3.
31.9 - Fk = 15.
Fk = 31.9 - 15 = 17.N. = Force of kinetic friction.

To find the frictional force, we'll need to consider the applied force and the acceleration of the box. Here are the steps to find the frictional force:

Step 1: Break down the force into its horizontal and vertical components.
We'll start by finding the horizontal component of the applied force. The horizontal component (Fh) can be found using the equation:
Fh = F * cos(theta)
where F is the magnitude of the force (40N) and theta is the angle (37 degrees). Substituting the values, we get:
Fh = 40N * cos(37°)

Step 2: Calculate the net force acting on the box.
The net force on the box is the force responsible for its acceleration. It can be calculated using the equation:
Net Force (Fn) = mass * acceleration
Given the mass of the box is 5kg and the acceleration is 3 m/s², substituting the values gives:
Fn = 5kg * 3m/s²

Step 3: Determine the frictional force.
Frictional force is the force that opposes the motion of the box. So, the frictional force (Ff) is equal to the horizontal component of the applied force minus the net force acting on the box. In equation form:
Ff = Fh - Fn

Now, let's substitute the values and calculate the frictional force:
Ff = (40N * cos(37°)) - (5kg * 3m/s²)

Simplifying the equation gives us:
Ff = (40N * 0.7986) - (5kg * 3m/s²)

After evaluating the expression, we find:
Ff ≈ 31.944 - 15

Hence, the frictional force must be approximately 16.944 Newtons.

Therefore, the answer is c) 17N.

To find the frictional force, we can start by breaking down the given information.

Given:
Force applied (F) = 40N
Angle above the horizontal (θ) = 37 degrees
Mass of the box (m) = 5kg
Acceleration (a) = 3 m/s^2

To solve for the frictional force, we need to find the net force acting on the box. The net force is the vector sum of the applied force and the force of friction.

Step 1: Find the horizontal component of the applied force.
Since the force is applied at an angle, we need to find its horizontal component (the force acting parallel to the floor). We can use trigonometry to do this.
Horizontal component of force (F_horizontal) = F * cos(θ)
F_horizontal = 40N * cos(37 degrees)
F_horizontal = 40N * 0.7986 (rounded to four decimal places)
F_horizontal ≈ 31.944N

Step 2: Calculate the net force.
The net force is the difference between the applied force and the force of friction.
Net force (F_net) = F_applied - F_friction
We know the net force is equal to the mass of the box multiplied by its acceleration.
F_net = m * a
F_net = 5kg * 3 m/s^2
F_net = 15N

Step 3: Calculate the force of friction.
Now, we can determine the force of friction by subtracting the horizontal component of the applied force from the net force.
F_friction = F_net - F_horizontal
F_friction = 15N - 31.944N
F_friction ≈ -16.944N

The negative sign indicates that the frictional force is acting in the opposite direction to the motion. Since the question asks for the magnitude (positive value) of the frictional force, we can disregard the negative sign.

Therefore, the magnitude of the frictional force that must be retarding the motion of the box is approximately 16.944N. However, since the given choices for the answers are rounded, the correct option would be d. 25N, which is the closest match.