Final answer:
The acceleration of a 45 kg box being pushed with a force of 250 N against a frictional force of 75 N is 3.89 m/s². This is calculated using Newton's second law of motion, a = F_net / m.
Step-by-step explanation:
To calculate the acceleration of a box across a floor, you need to use Newton’s second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass (a = F_net / m). In this case, we have a 45 kg box being pushed with a force of 250 N, while a sliding friction force of 75 N opposes this motion. The net force can be found by subtracting the friction force from the applied force (F_net = F_push - F_friction).
Using the provided values:
- Applied force (F_push) = 250 N
- Friction force (F_friction) = 75 N
- Mass of the box (m) = 45 kg
The net force (F_net) acting on the box is therefore F_push - F_friction, which is 250 N - 75 N = 175 N. To find the acceleration (a), we apply Newton’s second law:
a = F_net / m = 175 N / 45 kg = 3.89 m/s² (rounded to two decimal places).
Therefore, the acceleration of the box is 3.89 m/s².