A person pushes on a 60-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 0.68. (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.
+260 N because net force is zero
.68 (60)(9.81)
To solve this problem, we can apply Newton's second law of motion and the equation for static friction.
(a) To find the magnitude of the static frictional force, we need to compare the maximum static frictional force with the applied force.
The formula for static friction is given by:
Fs ≤ μs * Fn
Where:
Fs = static frictional force
μs = coefficient of static friction
Fn = normal force
In this case, the normal force is equal to the weight of the refrigerator, which is given by:
Fn = m * g
Where:
m = mass of the refrigerator
g = acceleration due to gravity
Plugging in the given values:
m = 60 kg
g = 9.81 m/s^2
Fn = 60 kg * 9.81 m/s^2
Fn = 588.6 N
Now, we can find the maximum static frictional force:
Fs ≤ 0.68 * 588.6 N
Fs ≤ 400.408 N
So, the magnitude of the static frictional force is 400.408 N.
Since the force applied is -260 N in the -x direction, the direction of the static frictional force is in the opposite direction, which is +x.
Therefore, the magnitude of the static frictional force is 400.408 N, and it acts in the +x direction.
(b) To find the magnitude of the largest pushing force that can be applied before the refrigerator starts to move, we need to determine the maximum value of the static frictional force.
The maximum static frictional force, before the refrigerator starts to move, is equal to the applied force that starts the motion. This force can be found using the formula:
F = μs * Fn
Plugging in the values:
F = 0.68 * 588.6 N
F = 400.408 N
Therefore, the magnitude of the largest pushing force that can be applied before the refrigerator just begins to move is 400.408 N.
To find the answers to this question, we need to use Newton's second law and the concept of static friction. Let's go step by step.
(a) If the refrigerator does not move, it means that the static friction force is equal in magnitude but opposite in direction to the applied force. In this case, the applied force is -260 N, which means it's in the -x direction. The static friction force will also be in the -x direction.
The formula for static friction force is given by:
Fs ≤ μs * N
where Fs is the static friction force, μs is the coefficient of static friction, and N is the normal force exerted by the floor on the refrigerator.
In this case, the normal force N is equal to the weight of the refrigerator, which is given by:
N = m * g
where m is the mass of the refrigerator and g is the acceleration due to gravity.
So, N = 60 kg * 9.81 m/s^2 = 588.6 N.
Now we can calculate the maximum static friction force:
Fs ≤ 0.68 * 588.6 N ≈ 400.25 N.
Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is approximately 400.25 N in the -x direction.
(b) To find the magnitude of the largest pushing force that can be applied before the refrigerator begins to move, we need to consider the maximum static friction force as the limiting factor.
The maximum pushing force before the refrigerator begins to move is equal to the maximum static friction force. So, the maximum pushing force is approximately 400.25 N.
Note: This is the maximum pushing force that can be applied without overcoming static friction. If a greater force is applied, the refrigerator will start moving and kinetic friction will be in effect, which is a different scenario.
That's it! We have found the magnitude and direction of the static frictional force and the maximum pushing force for the refrigerator.