What is the minimum horizontal force that needs to be applied to the bottom block of mass M so that the top block of mass m slides off? The coefficient of friction between the bottom block and the floor is µ1, the coefficient of friction between the two blocks is µ2
acceleration of both = a
force forward on top block = u2 m g = m a
so a = u2 g
force forward on bottom block = F
force back on top block = u2 m g + u1(m+M)g
F - u2 m g - u1(m+M)g= (m+M) a = (m+M) u2 g
F = u2 m g +u1 m g +u1 M g + u2 m g + u2 M g
= u1 (m + M) g + u2 ( 2m + M)g
Thank you!!!!
You are welcome.
To determine the minimum horizontal force required to make the top block slide off the bottom block, we need to consider the forces acting on both blocks.
Let's break down the forces acting on the blocks:
1. Bottom block (mass M):
- Weight (W1) acts vertically downward with a magnitude of M * g, where g is the acceleration due to gravity.
- Friction force (F1) opposing motion depends on the coefficient of friction (µ1) and the normal force (N1) acting on the bottom block from the floor.
2. Top block (mass m):
- Weight (W2) acts vertically downward with a magnitude of m * g.
- Friction force (F2) opposing motion depends on the coefficient of friction (µ2) and the normal force (N2) acting on the top block from the bottom block.
Now, in order for the top block to slide off the bottom block, the friction force (F2) between them must be overcome. This can be achieved by applying a horizontal force to the bottom block.
To find the minimum force required, we need to figure out the maximum friction force (F2) that can be generated between the two blocks. The maximum friction force can be calculated using the equation:
F2 = µ2 * N2,
where N2 is the normal force between the two blocks.
The normal force acting on the top block (N2) is equal to the weight of the top block because there is no vertical acceleration. Therefore, N2 = W2 = m * g.
Substituting this back into the equation for the maximum friction force, we get:
F2 = µ2 * (m * g).
Finally, the minimum horizontal force required to slide the top block off the bottom block is equal to the maximum friction force (F2), which is:
Minimum force = F2 = µ2 * (m * g).
So, the minimum horizontal force needed to make the top block slide off the bottom block is µ2 * (m * g).