A person pushes on a 56-kg refrigerator with a horizontal force of -251 N; the minus sign indicates that the force points in the −x direction. The coefficient of static friction is 0.7. (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 = 9.81 m/s2.

a. Wr = m * g = 56kg * 9.8N/kg = 549. N = Weight of refrigerator.

Fs = u*Wr = 0.7 * 549 = 384 N. = Force of static friction which points in the +x direction.

b. F = -384 N.

The value you calculated are wrong, units are ok though

To solve these problems, we need to consider the forces acting on the refrigerator and apply Newton's laws of motion. Let's break it down step-by-step.

(a) To find the magnitude and direction of the static frictional force, we first need to determine if the force applied is enough to overcome static friction and cause the refrigerator to move. If the refrigerator does not move, the magnitude of the applied force must be equal and opposite to the maximum static frictional force.

Step 1: Calculate the maximum static frictional force using the equation:
fs_max = μs * N
where μs is the coefficient of static friction and N is the normal force.

Step 2: Calculate the normal force acting on the refrigerator.
The normal force is equal to the weight of the refrigerator since it is on a horizontal surface and not accelerating vertically.
N = m * g
where m is the mass of the refrigerator and g is the acceleration due to gravity.

Given:
m = 56 kg
g = 9.81 m/s^2

Step 3: Calculate the maximum static frictional force.
fs_max = μs * N
fs_max = 0.7 * (56 kg * 9.81 m/s^2)

Calculate fs_max.

(b) To find the magnitude of the largest pushing force that can be applied before the refrigerator begins to move, we need to compare the applied force to the maximum static frictional force.

Step 4: Determine the applied force required to overcome static friction and set the refrigerator into motion.
f_applied = fs_max

Step 5: Calculate the magnitude of the largest pushing force.
The largest pushing force that can be applied before the refrigerator begins to move is equal to the magnitude of the applied force.

Now, let's go through the steps and calculate the results.

To solve this problem, we need to use the principles of static friction and apply Newton's laws. Here's how you can approach it:

(a) If the refrigerator does not move, it means that the force of static friction must be equal to the applied force in the opposite direction.

The formula for static friction is:
f_s = μ_s * N

where f_s is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force between the refrigerator and the floor.

To find the normal force, we need to use the equation:
N = m * g

where m is the mass of the refrigerator (56 kg) and g is the acceleration due to gravity (9.81 m/s^2).

Calculating N:
N = 56 kg * 9.81 m/s^2
N ≈ 549.36 N

Now, we can find the force of static friction:
f_s = 0.7 * 549.36 N
f_s ≈ 384.52 N

Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is approximately 384.52 N. Since the applied force is in the negative x-direction, the direction of the static frictional force is in the positive x-direction.

(b) To determine the magnitude of the largest pushing force that can be applied before the refrigerator starts moving, we need to find the maximum static frictional force. This force is given by:

f_max = μ_s * N

Using the same values as above, we can calculate:
f_max = 0.7 * 549.36 N
f_max ≈ 384.52 N

Therefore, the maximum pushing force that can be applied before the refrigerator starts moving is approximately 384.52 N.