A person pushes on a 62-kg refrigerator with a horizontal force of -280 N; the minus sign indicates that the force points in the -x direction. The coefficient of static friction is 0.70. (a) If the refrigerator does not move, what are the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? (b) What is the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move? Assume g = 9.8 m/s2.

(a) no acceleration so +280 N

(b)max friction force = 62*9.8*0.70
so -425 N

To solve this problem, we will first calculate the maximum static frictional force using the coefficient of static friction, and then check if the applied force is greater than the maximum static frictional force to determine if the refrigerator will move.

(a) To find the magnitude of the static frictional force, we'll use the formula:

F_static = μ * N

Where F_static is the static frictional force, μ is the coefficient of static friction, and N is the normal force.

The normal force is equal to the weight of the refrigerator, which can be calculated as:

N = m * g

Where m is the mass of the refrigerator and g is the acceleration due to gravity.

Given:
Mass of the refrigerator, m = 62 kg
Coefficient of static friction, μ = 0.70
Acceleration due to gravity, g = 9.8 m/s^2

Let's calculate the normal force first:

N = m * g
N = 62 kg * 9.8 m/s^2
N = 607.6 N

Now, we can calculate the magnitude of the static frictional force:

F_static = μ * N
F_static = 0.70 * 607.6 N
F_static = 425.32 N

The magnitude of the static frictional force is 425.32 N. The direction of the static frictional force is in the opposite direction to the applied force because it prevents the refrigerator from moving.

(b) To find the largest pushing force that can be applied before the refrigerator starts to move, we'll use the maximum static frictional force calculated in part (a).

If the applied force is greater than the maximum static frictional force, the refrigerator will start to move. Therefore, the largest pushing force F_max can be determined by:

F_applied = F_max

Given:
Applied force, F_applied = -280 N (negative sign indicates a force in the -x direction)

Since the applied force is negative, we have:

|F_applied| = |-280 N| = 280 N

Comparing the magnitude of the applied force with the maximum static frictional force:

280 N > 425.32 N

Since 280 N is less than 425.32 N, the refrigerator will not start to move.

Therefore, the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is 425.32 N.

To answer these questions, we need to understand the concept of static friction and how it relates to the given scenario. Let's break down each part one by one:

(a) If the refrigerator does not move, it means the static frictional force exerted by the floor on the refrigerator must be equal in magnitude but opposite in direction to the pushing force applied on it. The magnitude of the static frictional force is given by the equation:

|Ffriction| ≤ μs * |Fn|

where
|Ffriction| is the magnitude of the static frictional force
μs is the coefficient of static friction
|Fn| is the normal force

In this case, the pushing force is -280 N (negative sign indicates direction), and the coefficient of static friction is 0.70.

First, we need to find the normal force acting on the refrigerator. The normal force is the force exerted by a surface perpendicular to the object in contact with it. Since the refrigerator is on a horizontal surface, the normal force is equal to the weight of the refrigerator:

|Fn| = mg

where
m = mass of the refrigerator = 62 kg
g = acceleration due to gravity = 9.8 m/s²

|Fn| = (62 kg) * (9.8 m/s²)
|Fn| ≈ 607.6 N

Next, we can calculate the maximum static frictional force using the coefficient of static friction:

|Ffriction| ≤ μs * |Fn|
|Ffriction| ≤ (0.70) * (607.6 N)
|Ffriction| ≤ 425.32 N

Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is approximately 425.32 N. The direction of the static frictional force is opposite to the direction of the applied force, which is in the -x direction.

(b) The largest pushing force that can be applied before the refrigerator starts to move is when the static frictional force reaches its maximum value.

|Ffriction| = μs * |Fn|
Fpush - |Ffriction| = 0

We can rearrange this equation to solve for the maximum pushing force:

Fpush = μs * |Fn|

Fpush = (0.70) * (607.6 N)
Fpush ≈ 425.32 N

Therefore, the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is approximately 425.32 N.