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.
See previous post.
Well, it sounds like Sophia and the box are having quite the push-and-slide party! Let me crunch the numbers and see if they're keeping up with your demonstration.
To start, we need to know Newton's second law:
Force = mass * acceleration
In this case, the force exerted by Sophia is 40 N, and the mass of the box is 8 kg. So, we can rearrange the equation to solve for acceleration:
acceleration = force / mass
Plugging in the numbers, we get:
acceleration = 40 N / 8 kg
acceleration = 5 m/s^2
Oh, dear. It seems like I messed up my calculations along the way. Let me give it another shot.
Taking into account the friction force of 24 N, we can determine the net force acting on the box using Newton's second law:
Net force = applied force - friction force
Net force = 40 N - 24 N
Net force = 16 N
Now, we can calculate the acceleration using the revised equation:
acceleration = net force / mass
acceleration = 16 N / 8 kg
acceleration = 2 m/s^2
Ah, there we go! It appears my overly comedian calculations caused some confusion. The box indeed accelerates at a rate of 2 m/s^2. Thank you for your patience, and sorry for the bump in the road.
To show that the box accelerates at 2 m/s², we need to calculate the net force acting on the box and then use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's determine the net force acting on the box. The net force is the vector sum of all the forces acting on an object.
Given:
- Horizontal force exerted by Sophia, F_sophia = 40 N
- Frictional force acting on the box, F_friction = 24 N
To determine the net force, we subtract the frictional force from the force exerted by Sophia:
Net force = F_sophia - F_friction
Net force = 40 N - 24 N
Net force = 16 N
Now, we can apply Newton's second law of motion using the following formula:
Net force = mass * acceleration
Rearranging the formula, we have:
Acceleration = Net force / Mass
Plugging in the values we obtained:
Acceleration = 16 N / 8 kg
Acceleration = 2 m/s²
Therefore, the box accelerates at 2 m/s².
In summary, we calculated the net force acting on the box by subtracting the frictional force from the force exerted by Sophia. We then applied Newton's second law of motion to find the acceleration of the box, which turned out to be 2 m/s².