A person pushes on a 62-kg refrigerator with a horizontal force of -256 N; the minus sign indicates that the force points in the −x direction. The coefficient of static friction is 0.61.
(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?
Static frictional force =
(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.
Magnitude of largest force =
a. if it is not moving, it is pushing back with the same force you are pushing with, here, 256N
b. Forcefrictionmax= mu*m*g
To find the magnitude and direction of the static frictional force and the magnitude of the largest pushing force, we can use the following steps:
(a) If the refrigerator does not move, the static frictional force must be equal in magnitude and opposite in direction to the applied force. Therefore, it will exert a force in the positive x-direction.
To find the magnitude of the static frictional force, we can use the formula:
Static frictional force ≤ coefficient of static friction × normal force
The normal force is the force exerted by the floor on the refrigerator, which is equal in magnitude and opposite in direction to the gravitational force.
Normal force = mass × acceleration due to gravity = 62 kg × 9.81 m/s^2 = 607.02 N
Static frictional force ≤ 0.61 × 607.02 N
Now, we can calculate the magnitude of the static frictional force as:
Static frictional force = 0.61 × 607.02 N = 370.9422 N
Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is 370.9422 N, in the positive x-direction.
(b) To find the magnitude of the largest pushing force that can be applied before the refrigerator just begins to move, we need to reach the maximum static frictional force that the floor can provide.
The magnitude of the largest force can be found by setting the static frictional force equal to the maximum value, which is given by:
Max static frictional force = coefficient of static friction × normal force
Max static frictional force = 0.61 × 607.02 N
Now, we can calculate the magnitude of the largest pushing force as:
Magnitude of largest force = 0.61 × 607.02 N = 370.9422 N
Therefore, the magnitude of the largest pushing force that can be applied before the refrigerator begins to move is 370.9422 N.
To solve this problem, we need to consider the forces acting on the refrigerator and analyze the conditions for static friction.
(a) The magnitude of the static frictional force is equal to the force applied on the refrigerator until it reaches its maximum value. Since the refrigerator is not moving, the static frictional force must cancel out the applied force.
Given:
Mass of the refrigerator (m) = 62 kg
Force applied (F_applied) = -256 N
Coefficient of static friction (μ_s) = 0.61
To find the static frictional force (F_friction), we can use the equation:
F_friction = μ_s * N
where N is the normal force exerted on the refrigerator. The normal force is equal to the weight of the refrigerator, which is given by:
N = m * g
where g is the acceleration due to gravity.
Substituting the values into the equations, we get:
N = (62 kg) * (9.81 m/s^2) = 607.02 N
F_friction = (0.61) * (607.02 N) = 370.66 N
Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is 370.66 N. Since the applied force is in the negative x-direction, the static frictional force is in the positive x-direction.
(b) The magnitude of the largest pushing force (F_max) that can be applied to the refrigerator before it just begins to move is equal to the maximum static frictional force. This force can be found using the equation:
F_max = μ_s * N
Substituting the values into the equation, we get:
F_max = (0.61) * (607.02 N) = 370.66 N
Therefore, the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is 370.66 N.