If the coefficients of static and kinetic friction between a 20 kg block that sits on top of a 100 kg block are both essentially the same value of 0.5, determine the acceleration of each block for a force pulling on A of 60 N. Bottom block sits on a friction-less floor.
(I was able to figure out that block A accelerates 1.095 m/s^2 in the +x direction...but I cant seem to figure out acceleration for bottom block, block B.)
Shut up
@Sipho, if you'd like to continue using this site you may need to limit the kinds of post you are making. "Shut up" is not an effective response to a question you may not understand. You might want to not write anything and just shut up.
To determine the acceleration of the bottom block, Block B, we need to use the concept of friction. Since the bottom block sits on a friction-less floor, there will be no horizontal force acting on it except for the force exerted by the top block, Block A.
Let's break down the forces acting on the system consisting of Block A and Block B:
1. Force applied on Block A (F_applied) = 60 N (given)
2. Weight of Block A (W_A) = mass_A * g = 20 kg * 9.8 m/s^2 = 196 N
3. Normal force on Block A (N_A) = W_A = 196 N (since Block A is resting on Block B)
4. Friction force on Block A (F_friction,A) = coefficient_static * N_A = 0.5 * 196 N = 98 N (using the coefficient of static friction)
(Note: Initially, the force of static friction will be acting in the opposite direction of the applied force, preventing Block A from moving.)
Now, let's calculate the acceleration of Block A using Newton's second law: ΣF = m_A * a_A
Where ΣF is the sum of the forces acting on Block A.
ΣF = F_applied - F_friction,A
= 60 N - 98 N = -38 N (negative sign indicates opposing direction)
-38 N = m_A * a_A
-38 N = 20 kg * a_A
a_A = -1.9 m/s^2 (negative sign indicates opposing direction)
Therefore, the acceleration of Block A is -1.9 m/s^2 (opposite to the direction of the applied force).
Now, since Block B experiences an equal and opposite force to that of Block A, the acceleration of Block B will be the same.
Therefore, the acceleration of Block B is also -1.9 m/s^2 (opposite to the direction of the applied force).
Hence, both Block A and Block B accelerate at a rate of -1.9 m/s^2 (opposite to the direction of the applied force).