Three blocks on a rough horizontal surface are moving while in contact with each other as shown below. A force F = 215 N is applied to block m1. What is the force with which block m1 pushes on block m2? Coefficient of kinetic friction with floor is 0.34 (Hint: do not forget about third newton’s law!)
To find the force with which block m1 pushes on block m2, we need to consider the third law of motion, which states that for every action, there is an equal and opposite reaction.
Let's break down the problem and solve it step by step:
Step 1: Identify the known values and variables:
- Force applied to block m1 (F) = 215 N
- Coefficient of kinetic friction with the floor (μ) = 0.34
Step 2: Determine the force of friction:
The force of friction can be calculated by multiplying the coefficient of friction (μ) by the normal force (N). In this case, since the blocks are in contact horizontally, the normal force for each block is equal to its weight.
- Normal force on block m1 (N1) = mass of m1 × acceleration due to gravity
- Normal force on block m2 (N2) = mass of m2 × acceleration due to gravity
Step 3: Calculate the normal forces:
Since the normal forces are given by the weight of each block, we can calculate them as:
- Normal force on block m1 (N1) = mass of m1 × acceleration due to gravity
- Normal force on block m2 (N2) = mass of m2 × acceleration due to gravity
- Normal force on block m3 (N3) = mass of m3 × acceleration due to gravity
Step 4: Determine the force with which block m1 pushes on block m2:
According to Newton's third law, the force with which block m1 pushes on block m2 is equal in magnitude but opposite in direction to the force with which block m2 pushes on block m1. Therefore, the force with which block m1 pushes on block m2 is the same as the force with which block m2 pushes on block m1.
So, the force with which block m1 pushes on block m2 = F.
Therefore, the force with which block m1 pushes on block m2 is 215 N.