Box M2 sits atop M1. (M1=25kg M2=15kg). The coefficient of friction between boxes and between M1 and the ground is Uk=.4 and Us=.5. I found that 353N is the maximum force you can apply to box 1 so that box 2 doesn't slip off. Now it asks for the acceleration of M1 and M2 if the force is doubled to 706, knowing that box M2 will slip off of M1. Plugging in 706 for F into F=ma does not work. How can this be solved?
To solve this problem, we need to consider the forces acting on the system and the limiting factor that causes the slip.
First, let's calculate the maximum force that can be applied to box 1 (F_max) using the coefficient of friction (Uk) between box 2 and M1. The equation for this is:
F_max = Uk * (normal force between box 2 and M1)
The normal force between box 2 and M1 can be calculated as the weight of box 2, which is given by:
Weight of box 2 = mass of box 2 * acceleration due to gravity
Normal force between box 2 and M1 = Weight of box 2
Next, we need to determine the acceleration of M1 and M2 when the force is doubled to 706N. To find this, we'll use the equation:
Net force = (mass of M1 + mass of M2) * acceleration
The net force acting on the system is the applied force (706N) minus the force of static friction (Fs) between M1 and the ground. The force of static friction can be calculated with the equation:
Fs = Us * (normal force between M1 and the ground)
The normal force between M1 and the ground can be calculated as the weight of M1:
Weight of M1 = mass of M1 * acceleration due to gravity
Normal force between M1 and the ground = Weight of M1
Once we have calculated Fs, we can use the equation for net force to find the acceleration of the system.
Let's go through the steps:
Step 1: Calculate the maximum force that can be applied to box 1 (F_max):
- F_max = Uk * (normal force between box 2 and M1)
- Normal force between box 2 and M1 = Weight of box 2
Step 2: Find the weight of box 2:
- Weight of box 2 = mass of box 2 * acceleration due to gravity
Step 3: Calculate the normal force between box 2 and M1:
- Normal force between box 2 and M1 = Weight of box 2
Step 4: Determine the force of static friction between M1 and the ground (Fs):
- Fs = Us * (normal force between M1 and the ground)
- Normal force between M1 and the ground = Weight of M1
Step 5: Calculate the net force acting on the system:
- Net force = 706N - Fs
Step 6: Determine the acceleration of the system:
- Net force = (mass of M1 + mass of M2) * acceleration
By following these steps, we can find the acceleration of M1 and M2 when the force is doubled to 706N.