What is the minimum downward force on the box in the figure that will keep it from slipping? The coefficients of static and kinetic friction between the box and the floor are 0.30 and 0.20, respectively.
There must be some sort of configuration here in a picture, or something. Surely the box has a moving force being applied.
Oh, the box must be so clingy! Well, to prevent it from slipping, we need to consider the forces at play. Let's do some clown calculations here.
We know that the coefficient of static friction (μs) is 0.30, and since the box is on the verge of slipping, the force of static friction (fs) will be the maximum value.
fs = μs * N
Now, to find out the minimum downward force required (let's call it "W"), we need to calculate the normal force (N) first.
N = mg
where m is the mass of the box and g is the acceleration due to gravity. Now, taking into account the kinetic friction coefficient (μk), we can calculate the force of kinetic friction (fk) when the box is actually moving.
fk = μk * N
Since the box is not slipping, the maximum static friction fs is equal to the force of kinetic friction fk.
fs = fk
μs * N = μk * N
μs = μk
Therefore, the minimum downward force required to prevent slipping is W = mg.
So, my dear querent, the minimum downward force needed is equal to the weight of the box. Just remember to be careful and avoid any banana peels along the way – that would definitely lead to slipping!
To determine the minimum downward force on the box that will keep it from slipping, we need to consider the forces acting on the box.
In this scenario, there are two types of friction coefficients to consider - static friction and kinetic friction. Static friction is the friction between two surfaces when there is no relative motion between them, while kinetic friction is the friction when there is relative motion.
Let's assume the weight of the box is W. The forces acting on the box are:
1. Weight (mg): This is the force exerted by the Earth on the box and is equal to the mass of the box (m) multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s^2.
Therefore, Weight (mg) = W.
2. Normal force (N): This is the force exerted by the floor on the box in the upward direction. It is equal in magnitude and opposite in direction to the weight of the box.
Therefore, Normal force (N) = W.
To prevent the box from slipping, the force of static friction between the box and the floor must be equal to or greater than the force trying to make it slip. The maximum force of static friction (F_static) is given by the formula:
F_static = friction coefficient (static friction) * Normal force (N)
In this case, the static friction coefficient is given as 0.30. Therefore,
F_static = 0.30 * N (since N = Weight (W))
The minimum downward force on the box that will keep it from slipping is when the force applied downwards (F_applied) is equal to the maximum force of static friction (F_static).
Therefore, F_applied = F_static = 0.30 * N = 0.30 * W
Substituting N = W (since the normal force is equal to the weight of the box), we get:
F_applied = F_static = 0.30 * W
So, the minimum downward force on the box that will keep it from slipping is 0.30 times the weight of the box.