Question

As Carlos and Manual both push a 4 kg box to the right across a rough floor, the box speeds up at a rate of 1.2 m/s2. If you assume that Manual pushes with a force strength of 8.0 N and the friction force of the floor on the box is 5.0 N, then what is the strength of the force that Carlos pushes on the box?

0.33 N
1.8 N
4.6 N
6.0 N

Answer 1

Carlos's force is determined to be 1.8 N. This is found by applying Newton's second law and accounting for the frictional force that opposes the combined force exerted by Carlos and Manual on the box.

Step-by-step explanation:

To find the strength of the force that Carlos pushes on the box, we use Newton's second law of motion, which states that the force exerted on an object equals its mass times its acceleration (F = ma).

As provided, the box accelerates at 1.2 m/s2, and its mass is 4 kg.

The total force exerted on the box to the right (Ftotal) can be calculated by multiplying the mass of the box (m) by its acceleration (a):

Ftotal = ma = 4 kg × 1.2 m/s2

= 4.8 N.

Since Manual exerts a force of 8.0 N and friction exerts an opposing force of 5.0 N, we can calculate the net force contributing to the acceleration by subtracting the friction force from Manual's force:

Fnet = Fmanual - Ffriction

= 8.0 N - 5.0 N

= 3.0 N.

Now, the sum of the forces by Carlos and Manual must equal the total force required for the acceleration of the box: Fcarlos + Fmanual = Ftotal.

Therefore, we can find Carlos's force by subtracting Manual's net force from the total required force: Fcarlos = Ftotal - Fnet = 4.8 N - 3.0 N = 1.8 N.