A 5kg box on a horizontal table is pushed by a horizontal force of 15N. If the coefficient of friction is 0.4, will the box move? what is the smallest force that could make the box slide along the table?

F=mk

F= m(mg)
F= 0.4(5)9.8
F= 19.6

the frictional force is

... 5 * 9.8 * .4

To determine if the box will move, we need to compare the force due to friction with the applied force. If the applied force is greater than the force of friction, the box will move.

1. Calculate the force of friction:
Frictional force = coefficient of friction * Normal force

The normal force is equal to the weight of the box, which can be calculated as:
Normal force = mass * gravitational acceleration

The gravitational acceleration is approximately 9.8 m/s².

Mass of the box = 5 kg

Normal force = 5 kg * 9.8 m/s² = 49 N

Frictional force = 0.4 * 49 N = 19.6 N

2. Compare the force of friction with the applied force:
Applied force = 15 N

The applied force is greater than the force of friction, so the box will move.

To determine the smallest force that can make the box slide along the table, we need to find the minimum force required to overcome static friction.

3. Calculate the maximum force of static friction:
Maximum force of static friction = coefficient of static friction * Normal force

The coefficient of static friction is typically higher than the coefficient of kinetic friction. However, we are not given the coefficient of static friction, so let's assume it is the same as the coefficient of kinetic friction, which is 0.4.

Maximum force of static friction = 0.4 * 49 N = 19.6 N

The smallest force that could make the box slide along the table is equal to the maximum force of static friction, which is 19.6 N.

To determine whether the box will move or not, we need to compare the applied force with the maximum static friction force. If the applied force is greater than or equal to the maximum static friction force, the box will move. Otherwise, it will remain at rest.

First, we calculate the maximum static friction force using the formula:

Maximum static friction force = coefficient of friction * normal force

The normal force is equal to the weight of the box since it is on a horizontal table. The weight is the mass of the box multiplied by the acceleration due to gravity:

Weight = mass * acceleration due to gravity

Weight = 5 kg * 9.8 m/s^2 = 49 N

The maximum static friction force can be calculated as:

Maximum static friction force = 0.4 * 49 N = 19.6 N

Since the applied force of 15 N is less than the maximum static friction force of 19.6 N, the box will not move.

Now, let's determine the smallest force that could make the box slide along the table. This can be done by calculating the kinetic friction force, as once the box starts moving, it experiences kinetic friction instead of static friction.

The kinetic friction force can be calculated as:

Kinetic friction force = coefficient of friction * normal force

Using the same normal force as before:

Kinetic friction force = 0.4 * 49 N = 19.6 N

Therefore, the smallest force that could make the box slide along the table is 19.6 N. Any force applied that is equal to or greater than this value will cause the box to slide.