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 189.0 N at an angle of 30.0◦ with the horizontal. The box has a mass of 39.0 kg, and the coefficient of kinetic friction between the box and floor is 0.370.

The acceleration due to gravity is 9.81 m/s2 .
What is the acceleration of the box? Answer in units of m/s2

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

Step 1: Calculate the gravitational force:
The gravitational force acting on the box can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity

In this case, the mass of the box is 39.0 kg and the acceleration due to gravity is 9.81 m/s^2. Plugging these values into the formula gives:
Force_gravity = 39.0 kg * 9.81 m/s^2 = 382.59 N

Step 2: Calculate the force of friction:
The force of friction can be calculated using the formula:
Force_friction = coefficient_of_friction * Force_normal

The coefficient of kinetic friction between the box and floor is given as 0.370. The normal force, denoted as Force_normal, is the perpendicular force exerted by the floor on the box, equal in magnitude to the gravitational force. Therefore, Force_normal = Force_gravity.

Plugging in the values, we get:
Force_friction = 0.370 * 382.59 N ≈ 141.71 N

Step 3: Calculate the net force:
The net force acting on the box is the vector sum of the applied force and the force of friction. Since the applied force and the force of friction are in opposite directions, we subtract the force of friction from the applied force.

Applied force = 189.0 N
Force_net = Applied force - Force_friction
= 189.0 N - 141.71 N
= 47.29 N (approx.)

Step 4: Calculate the acceleration:
Using Newton's second law of motion, we can calculate the acceleration by dividing the net force by the mass of the box:
acceleration = Force_net / mass

Plugging in the values, we get:
acceleration = 47.29 N / 39.0 kg ≈ 1.212 m/s^2

Therefore, the acceleration of the box is approximately 1.212 m/s^2.

ok, the upward force is 189sin30, which reduces normal force.

net force=mass*(acceleration)
189Cos30-.370*(39g-189*sin30)=39 a
solve for a