A person pushes on a 55-kg refrigerator with a horizontal force of -250 N; the minus sign indicates that the force points in the -x direction. The coefficient of static friction is 0.56. (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.
+250 :)
weight = m g = 55*9.8 = 539 Newtons
That is the normal force on the floor
Max friction = .56*539 = 302 N
To solve this problem, we need to apply Newton's second law and use the concept of static friction.
(a) To find the magnitude and direction of the static frictional force, we need to determine if the applied force is enough to overcome the force of static friction and start the motion. Since the refrigerator does not move, we know that the net force in the horizontal direction is zero.
Net force = Applied force + Force of static friction
In this case:
Net force = 0 N (since the refrigerator does not move)
Applied force = -250 N (negative because it points in the -x direction)
We can rewrite the equation as:
0 N = -250 N + Force of static friction
Rearranging the equation, we find:
Force of static friction = 250 N
Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is 250 N. The direction of the static frictional force is in the positive x-direction to oppose the applied force, which means it points to the right.
(b) To determine the largest pushing force before the refrigerator begins to move, we need to consider the maximum static frictional force. The maximum static frictional force is given by:
Force of static friction (max) = coefficient of static friction × Normal force
The normal force is equal to the weight of the refrigerator, which is given by:
Normal force = mass × gravity
Given:
mass = 55 kg
coefficient of static friction = 0.56
g = 9.8 m/s^2
Calculating the normal force:
Normal force = 55 kg × 9.8 m/s^2 = 539 N
Now we can substitute the values into the equation for the maximum static frictional force:
Force of static friction (max) = 0.56 × 539 N ≈ 301.84 N
Therefore, the largest pushing force that can be applied to the refrigerator before it just begins to move is approximately 301.84 N.