Sophia exerts a steady 40-N horizontal force on a 8-kg box resting on a lab bench. The box slides against a horizontal friction force of 24 N. Show that the box accelerates

at 2 m/s2.

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Fn = m*a = 40-24 = Net force.

8a = 16
a = 2 m/s^2.

Your answer is spot on.

Well, it seems like Sophia is putting in quite the effort to move that box. And she must have a pretty strong arm too if she can exert a 40-N force! But let's get down to business.

To determine the acceleration of the box, we need to consider the net force acting on it. The net force is equal to the difference between the applied force and the friction force. So, in this case, the net force is:

Net force = Applied force - Friction force
= 40 N - 24 N
= 16 N

Great! We've got the net force. Now, we can 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. In this case, the mass of the box is 8 kg. So, the equation becomes:

Acceleration = Net force / Mass
= 16 N / 8 kg
= 2 m/s²

Ta-da! The box is indeed accelerating at 2 m/s². Looks like Sophia's efforts are paying off. I hope she doesn't get too much of a "handle" on sliding boxes, though. Safety first!

To show that the box accelerates at 2 m/s^2, we need to calculate the net force acting on the box and then use Newton's second law of motion.

Step 1: Calculate the net force
The net force acting on an object is the vector sum of all the forces acting on it. In this case, the net force can be determined by subtracting the frictional force from the force exerted by Sophia.

Net force = Force exerted by Sophia - Frictional force
Net force = 40 N - 24 N
Net force = 16 N

Step 2: Apply Newton's second law of motion
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Acceleration = Net force / Mass
Acceleration = 16 N / 8 kg
Acceleration = 2 m/s^2

Therefore, the box accelerates at 2 m/s^2.

To summarize the calculation:
Net force = 40 N - 24 N = 16 N
Acceleration = Net force / Mass = 16 N / 8 kg = 2 m/s^2