A student pulls on a rope attached to a box of books and moves the box down the hall. The student pulls with a force of 182N at an angle of 25° above the horizontal. The box has a mass of 35kg and &mu k between the box and the floor is 0.27. What is the acceleration of the box.

69, 420

2.75

To find the acceleration of the box, 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.

Step 1: Calculate the net force acting on the box.
The net force can be determined by resolving the applied force into its horizontal and vertical components. The horizontal component of the force aids in moving the box, while the vertical component will not affect the box's motion along the horizontal direction.

Given that the applied force is 182N at an angle of 25° above the horizontal, we can find the horizontal component of the force using trigonometry.
Horizontal force = applied force * cos(angle)
Horizontal force = 182N * cos(25°)

Step 2: Determine the frictional force opposing the motion of the box.
The frictional force can be calculated using the formula:
Frictional force = coefficient of friction * normal force

The normal force is the force exerted by the surface on the box, which is equal to the weight of the box since there is no vertical acceleration (the box is not moving vertically).

Normal force = mass * gravitational acceleration
Normal force = 35kg * 9.8 m/s^2

Frictional force = coefficient of friction * normal force
Frictional force = 0.27 * (35kg * 9.8 m/s^2)

Step 3: Calculate the net force on the box.
The net force is the difference between the applied force and the frictional force since they act in opposite directions.
Net force = Horizontal force - Frictional force

Step 4: Calculate the acceleration of the box.
Using Newton's second law:
Net force = mass * acceleration

Solving for acceleration:
acceleration = net force / mass

Now we can substitute the values and calculate the acceleration of the box.

X = hor. = 182*cos25 = 164.9 N.

C.F. = 0.27 = 27% of force used to overcome friction. 73 % used to move
box:
F(net) = 0.73 * 164.9 = 120.4 N.

a = F(net) / m = 120.4 / 35 = 3.4 m/s^2

520.4368

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