Final answer:
To calculate the acceleration of the box, we need to find the net force by adding the x-components and y-components of the forces acting on the box. The x-component of the net force is 40 N, and the y-component is 0 N since there is no vertical force. Therefore, the acceleration of the box is approximately 1.0 m/s² to the right.
Step-by-step explanation:
To calculate the acceleration of the box, we need to 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. In this case, the box experiences two forces: 40 N at 0 degrees and 25 N at 180 degrees. These forces can be represented as vectors and added together to find the net force.
The net force can be found by adding the x-components and y-components of the forces separately. The x-component of the net force is the sum of the x-components of the forces, which is 40 N * cos(0 degrees) + 25 N * cos(180 degrees). The y-component of the net force is the sum of the y-components of the forces, which is 40 N * sin(0 degrees) + 25 N * sin(180 degrees).
Once we have the net force, we can use Newton's second law to find the acceleration. The mass of the box is 2000 grams, which is equal to 2 kilograms. Therefore, the acceleration can be calculated as follows:
acceleration = net force / mass
Let's calculate the x-component and y-component of the net force:
x-component of the net force = 40 N * cos(0 degrees) + 25 N * cos(180 degrees) = 40 N
y-component of the net force = 40 N * sin(0 degrees) + 25 N * sin(180 degrees) = 0 N
Since there is no vertical force acting on the box, the acceleration will only be in the x-direction. Therefore, the acceleration of the box is approximately 1.0 m/s² to the right.