A clerk moves a box of cans down an aisle by pulling on a strap attached to the box. The clerk pulls with a force of 174.0 N at an angle of 27.0 degrees with the horizontal. The box has a mass of 39.0 kg, and the coefficient of kinetic friction between the box and floor is 0.530. The acceleration of gravity is 9.81 m/s2 . What is the acceleration of the box? Answer in units of m/s2.

Well, isn't this a pickle! We have a clerk playing tug-of-war with a box of cans. Let's see if we can figure out the acceleration of this gripping saga.

First, we need to find the force of friction acting on the box. We can do that by multiplying the coefficient of kinetic friction (0.530) with the normal force. Now, the normal force is simply the weight of the box, which is the mass (39.0 kg) multiplied by the acceleration due to gravity (9.81 m/s2).

So, the normal force = 39.0 kg * 9.81 m/s2 = 382.59 N.

Now, we can calculate the force of friction = 0.530 * 382.59 N = 202.33 N.

Since the clerk is pulling the box with a force of 174.0 N at an angle of 27.0 degrees with the horizontal, we need to resolve this force into horizontal and vertical components.

The horizontal component of the pulling force = 174.0 N * cos(27.0 degrees) = 149.53 N.

Now, the net force acting on the box in the horizontal direction is the difference between the applied force and the force of friction.

Net force = Applied force - Force of friction
Net force = 149.53 N - 202.33 N
Net force = -52.80 N (negative sign indicates opposite direction)

Finally, we can use Newton's second law (F = ma) to find the acceleration of the box.

-52.80 N = 39.0 kg * a
a = -52.80 N / 39.0 kg
a ≈ -1.35 m/s2

Voila! The acceleration of the box is approximately -1.35 m/s2. Note the negative sign indicates that the box is moving in the opposite direction to the applied force. Keep your balance, dear clerk!

To find the acceleration of the box, we need to calculate the net force acting on the box.

First, let's calculate the force of friction opposing the motion of the box. We do this using the equation:

Force of friction = coefficient of kinetic friction * normal force

The normal force is given by the equation:

Normal force = mass of the box * acceleration due to gravity

Normal force = 39.0 kg * 9.81 m/s^2 = 382.59 N

Force of friction = 0.530 * 382.59 N = 202.5297 N

Next, we need to find the horizontal component of the applied force. We do this by multiplying the applied force by the cosine of the angle:

Horizontal component of applied force = 174.0 N * cos(27.0 degrees) = 152.962 N

The net force is calculated by subtracting the force of friction from the horizontal component of the applied force:

Net force = Horizontal component of applied force - Force of friction
Net force = 152.962 N - 202.5297 N = -49.5677 N

Since the net force is negative, we can infer that the direction of the acceleration is opposite to the direction of the applied force.

Finally, we can calculate the acceleration using Newton's second law of motion:

Net force = mass of the box * acceleration
-49.5677 N = 39.0 kg * acceleration

Solving for acceleration:

acceleration = -49.5677 N / 39.0 kg = -1.2704 m/s^2

Therefore, the acceleration of the box is approximately -1.2704 m/s².

To find the acceleration of the box, we need to consider the forces acting on it. Let's break it down step by step.

1. Determine the gravitational force acting on the box:
The gravitational force is given by the formula: F_gravity = m * g, where m is the mass of the box (39.0 kg) and g is the acceleration due to gravity (9.81 m/s^2).
F_gravity = 39 * 9.81 = 382.59 N

2. Determine the force of friction:
The force of friction can be found using the formula: F_friction = μ * F_normal, where μ is the coefficient of kinetic friction (0.530) and F_normal is the normal force acting on the box.
The normal force is equal to the gravitational force (F_gravity = 382.59 N) acting vertically upward.
F_friction = 0.530 * 382.59 = 202.72 N

3. Resolve the applied force into component vectors:
The applied force can be split into vertical and horizontal components. The vertical component is F_vertical = F_applied * sin(θ), where θ is the angle of the applied force with the horizontal (27.0 degrees). The horizontal component is F_horizontal = F_applied * cos(θ).
F_vertical = 174.0 * sin(27.0) = 77.21 N
F_horizontal = 174.0 * cos(27.0) = 148.91 N

4. Determine the net force on the box along the horizontal direction:
The net force is the difference between the horizontal component of the applied force and the force of friction.
Net force = F_horizontal - F_friction = 148.91 - 202.72 = -53.81 N
(Note that the negative sign indicates the opposing direction.)

5. Apply Newton's second law to find the acceleration:
Newton's second law states that the net force on an object is equal to its mass multiplied by its acceleration: Net force = m * a.
Rearranging the equation, we find: a = Net force / m.
a = -53.81 / 39.0 = -1.38 m/s^2

So, the acceleration of the box is approximately -1.38 m/s^2, where the negative sign indicates that the box is experiencing deceleration.