A block M1 of mass 13.0 kg sits on top of a larger block M2 of mass 23.0 kg which sits on a flat surface. The kinetic friction coefficient between the upper and lower block is 0.440. The kinetic friction coefficient between the lower block and the flat surface is 0.140. A horizontal force F = 92 N pushes against the upper block, causing it to slide. The friction force between the blocks then causes the lower block to slide also. Find the magnitude of the acceleration of the lower block
Hint: The acceleration of the upper block is 2.764923077 m/s^2
To find the magnitude of the acceleration of the lower block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's calculate the net force acting on the upper block (M1) using the given force (F = 92 N) and the kinetic friction coefficient between the upper and lower block (μ1 = 0.440). The friction force between the two blocks opposes the applied force.
The friction force between the upper and lower block is given by the formula:
Friction force (Ff1) = μ1 * normal force
The normal force is equal to the weight of the upper block (M1).
Normal force (N1) = M1 * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values:
N1 = 13.0 kg * 9.8 m/s^2 = 127.4 N
Ff1 = 0.440 * 127.4 N = 56.1 N
Since the applied force (F = 92 N) is larger than the friction force (Ff1), there is still a net force acting on the upper block. Therefore, the upper block will accelerate.
Now, let's calculate the acceleration of the upper block (a1). Using Newton's second law:
Net force (Fnet1) = M1 * a1
The net force is the difference between the applied force and the friction force:
Fnet1 = F - Ff1
= 92 N - 56.1 N
= 35.9 N
Plugging in the values:
35.9 N = 13.0 kg * a1
Solving for a1:
a1 = 35.9 N / 13.0 kg
= 2.764923077 m/s^2
We are given that the acceleration of the upper block is 2.764923077 m/s^2.
Since the upper and lower blocks are connected, they will have the same acceleration. Therefore, the magnitude of the acceleration of the lower block is also 2.764923077 m/s^2.