A box of mass 25kg is sitting on a horizontal plane and has a normal force pointing down of 31N, and the coeff of kinetic and static friction between the box and floor are .22 and .38, respectively. What is the min horizontal force F needed to make the box start moving?
Fn = 31N. = Normal force.
Fs = u*Fn = 0.38 * 31 = 11.78 N. = Force of static friction.
F-Fs = M*a.
F-11.78 = 25*0
F = 11.78 N.
To find the minimum horizontal force needed to make the box start moving, we need to consider the forces acting on the box.
First, let's list the forces acting on the box:
1. Weight (mg): The force due to gravity acting vertically downward. Its magnitude is given by the mass of the box (m) multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²). Since the normal force is pointing down, we know that the weight is equal to 31 N.
2. Normal Force (N): The force exerted by the plane perpendicular to the surface of contact. It acts vertically upward, opposing the weight of the box. The given normal force is 31 N.
3. Static Friction (fs): The force that resists the motion of two surfaces in contact when they are not in relative motion. It acts parallel to the surface of contact and opposes the applied force. The static friction force has a maximum value and depends on the coefficient of static friction (µs) and the normal force (N). The coefficient of static friction between the box and the floor is given as 0.38, so the static friction force (fs) is equal to 0.38 times the normal force.
4. Kinetic Friction (fk): The force that opposes the motion of two surfaces in contact when they are already in relative motion. Like static friction, it acts parallel to the surface of contact and opposes the applied force. The kinetic friction force depends on the coefficient of kinetic friction (µk) and the normal force (N). The coefficient of kinetic friction between the box and the floor is given as 0.22, so the kinetic friction force (fk) is equal to 0.22 times the normal force.
To find the minimum horizontal force needed to make the box start moving, we need to compare the maximum static friction force (fs) to the applied force (F). Once the applied force exceeds the maximum static friction force, the box will start moving. Mathematically, this can be expressed as:
F > fs
Since fs = µs * N, and N = 31 N, we can substitute these values:
F > 0.38 * 31
Calculating the right side of the inequality:
F > 11.78 N
Therefore, the minimum horizontal force needed to make the box start moving is greater than 11.78 Newtons.