A person pushes on a 59-kg refrigerator with a horizontal force of -260 N; the minus sign indicates that the force points in the -x direction. The coefficient of static friction is 0.60. (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.

If it does not move, the friction the floor exerts is +260N.

largest pushing force:
force=mu*mg=.6*58*9.8 N

M*g = 59 * 9.8 = 578 N. = Wt. of refrig. = Normal force(Fn).

a. Fs = u*Fn = 0.6 * 578 = 347 N.(+x direction) = Force of static friction.

b. F - Fs = M*a.
F - 347 = 59 * 0,
F = 347 N.

To solve this problem, we'll use the following equations:

(a) The magnitude of the static frictional force (Fs) is given by:

Fs = μs * N

where μs is the coefficient of static friction and N is the normal force.

(b) The maximum pushing force (Fmax) before the refrigerator begins to move is equal to the product of the coefficient of static friction (μs) and the normal force (N):

Fmax = μs * N

We'll use these equations to find the solutions step by step.

Step 1: Calculate the normal force (N).
Since the refrigerator is on the horizontal surface and not accelerating vertically, the normal force is equal to the weight of the refrigerator, given by:

N = m * g

where m is the mass of the refrigerator and g is the acceleration due to gravity. Plugging in the values:

m = 59 kg
g = 9.8 m/s^2

N = 59 kg * 9.8 m/s^2
N = 578.2 N

So, the normal force exerted by the floor on the refrigerator is 578.2 N.

Step 2: Calculate the magnitude and direction of the static frictional force (Fs).
Plugging in the values into the equation for Fs:

Fs = μs * N
Fs = 0.60 * 578.2 N
Fs = 346.92 N

The magnitude of the static frictional force is 346.92 N.

The direction of the static frictional force is opposite to the direction of the applied force (-x direction in this case) to prevent the refrigerator from sliding.

Therefore, the direction of the static frictional force is in the +x direction.

Step 3: Calculate the magnitude of the largest pushing force (Fmax).
Using the equation for Fmax:

Fmax = μs * N
Fmax = 0.60 * 578.2 N
Fmax = 346.92 N

The magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is 346.92 N.

So, the answers to the given questions are:
(a) The magnitude of the static frictional force is 346.92 N, and its direction is in the +x direction.
(b) The magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is 346.92 N.

(a) To find the magnitude and direction of the static frictional force that the floor exerts on the refrigerator, we need to understand the conditions for static friction.

The maximum static friction is calculated using the formula:

\( f_{\text{{max}}} = \mu_s N \)

Where:
\( f_{\text{{max}}} \) is the maximum static frictional force,
\( \mu_s \) is the coefficient of static friction,
and \( N \) is the normal force.

The normal force is the force exerted by the floor perpendicular to the surface of the refrigerator and is given by:

\( N = mg \)

Where:
\( m \) is the mass of the refrigerator,
and \( g \) is the acceleration due to gravity.

Plugging in the given values:

\( m = 59 \) kg
\( g = 9.8 \) m/s²
\( \mu_s = 0.60 \)

First, calculate the normal force:

\( N = mg = 59 \, \text{{kg}} \times 9.8 \, \text{{m/s²}} = 578.2 \, \text{{N}} \)

Next, calculate the maximum static friction:

\( f_{\text{{max}}} = \mu_s N = 0.60 \times 578.2 \, \text{{N}} = 346.92 \, \text{{N}} \)

Since the refrigerator does not move, the static frictional force opposes the applied force and has the same magnitude but the opposite direction:

\( f_{\text{{static friction}}} = -346.92 \, \text{{N}} \) (in the +x direction)

Therefore, the magnitude of the static frictional force is \( 346.92 \, \text{{N}} \) and it acts in the +x direction.

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

\( f_{\text{{max}}} = \mu_s N \)

Using the same values as before:

\( \mu_s = 0.60 \)
\( N = 578.2 \) N

\( f_{\text{{max}}} = 0.60 \times 578.2 \) N
\( f_{\text{{max}}} = 346.92 \) N

The magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is \( 346.92 \) N.