A person pushes on a 56-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 0.58.
(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.
To solve this problem, we need to consider the forces acting on the refrigerator and use Newton's laws.
(a) If the refrigerator is not moving, the static frictional force must be equal in magnitude and opposite in direction to the applied force, so that the net force on the refrigerator is zero. Mathematically, we can express this as:
|f_friction| = |f_applied|
where |f_friction| is the magnitude of the static frictional force, and |f_applied| is the magnitude of the applied force.
So, in this case, the magnitude of the static frictional force that the floor exerts on the refrigerator is 260 N, and the direction is in the positive x-direction.
(b) To determine the maximum pushing force before the refrigerator starts to move (i.e., the limiting force of static friction), we need to take into account the coefficient of static friction (μ_s) and the weight of the refrigerator (mg).
The formula for static friction is:
f_friction = μ_s * N
where f_friction is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force acting on the object.
The normal force, N, can be calculated using the weight of the refrigerator (mg) and assuming it is on a level surface, as:
N = mg
Substituting the value of N into the equation for static friction, we have:
f_friction = μ_s * mg
Given values:
μ_s = 0.58
m = 56 kg
g = 9.8 m/s^2
f_friction = 0.58 * 56 kg * 9.8 m/s^2
Simplifying the equation, we find that the magnitude of the maximum pushing force is approximately 319.624 N. Therefore, the largest pushing force that can be applied to the refrigerator before it begins to move is approximately 319.624 N.
To answer these questions, we need to understand the concepts of static friction and the conditions for an object to start moving.
(a) If the refrigerator does not move, the static frictional force exerted by the floor on the refrigerator balances the applied force. So, in this case, the static frictional force has the same magnitude as the applied force but with an opposite direction.
To find the magnitude of the static frictional force, we can use the formula:
F_friction = μ_s * F_normal
Where:
- F_friction is the frictional force
- μ_s is the coefficient of static friction
- F_normal is the normal force
The normal force is equal to the weight of the refrigerator, which can be calculated by multiplying the mass (m) with the acceleration due to gravity (g):
F_normal = m * g
Given that the mass of the refrigerator is 56 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the normal force:
F_normal = 56 kg * 9.8 m/s^2 = 548.8 N
Now, we can find the magnitude of the static frictional force:
F_friction = 0.58 * 548.8 N = 318.3 N
Therefore, the magnitude of the static frictional force that the floor exerts on the refrigerator is 318.3 N, and its direction is opposite to the applied force (-x direction).
(b) To determine the magnitude of the largest pushing force before the refrigerator starts moving, we need to find the maximum value of static friction, which is given by:
F_friction_max = μ_s * F_normal
Using the same values as above, we can calculate the maximum static frictional force:
F_friction_max = 0.58 * 548.8 N = 318.3 N
Therefore, the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is 318.3 N.
a. M*g = 56 * 9.8 = 548.8 N. = Wt. of refrigerator = Normalforce(Fn).
Fs = u*Fn = 0.58 * 549 = 318.3 N. = Force of static friction.
b. Fap-Fs = M*a
Fap - 318.3 = M*0 = 0
Fap = 318.3 = Force applied.