A force of 75 N is applied to two boxes stacked on top of each other. The coefficient of kinetic friction between the bottom box and the floor is 0.3. If the box on top is to accelerate at the same rate as the box on the bottom, what must the minimum coefficient of static friction between the two boxes be?
I guess you push the bottom one? mb is bottom mass, mt the top
75 - .3 (mb+mt) g = (mb + mt)a
a = [75 -.3(mb+mt)g]/(mb+mt)
max friction force on mt = mu mt g = mt a
mu g = a
so
mu = [ 75/g -.3(mb+mt)] /(mb+mt)
To determine the minimum coefficient of static friction between the two boxes, we need to first understand the forces acting on each box and how they relate to each other.
Let's start with the bottom box. The force applied to it is 75 N. There are two main forces acting on the bottom box: the applied force (75 N) and the force of kinetic friction between the box and the floor.
The force of kinetic friction (Fk) can be determined using the equation:
Fk = μk * N
Where μk is the coefficient of kinetic friction and N is the normal force.
Since the box is on a flat surface and not accelerating vertically, the normal force (N) is equal to the weight (mg) of the bottom box, which can be calculated using:
mg = m * g
Where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, let's move on to the top box. If it is to accelerate at the same rate as the bottom box, there must be a force acting on it in the forward direction. This force is the force of static friction (Fs) between the two boxes.
The force of static friction (Fs) can be calculated using the equation:
Fs = μs * N
Where μs is the coefficient of static friction and N is the normal force acting on the top box.
Since the top box is not in contact with the floor, its normal force (N) is equal to the weight (mg) of only the top box, which can be calculated as above.
Now, to ensure that the top box accelerates at the same rate as the bottom box, the force of static friction (Fs) must be equal to the applied force (75 N). Therefore, we can set up the following equation:
μs * N = 75
Substituting N with the weight of the top box (mg) and rearranging the equation, we have:
μs * m * g = 75
Now, we can solve for the minimum coefficient of static friction (μs) by dividing both sides of the equation by m * g:
μs = 75 / (m * g)
So, to find the minimum coefficient of static friction between the two boxes, we need to know the mass of the top box (m).