Two blocks are in contact on a frictionless table. A horizontal force F is applied to M2, as shown. If M1 = 1.06 kg, M2 = 3.80 kg, and F = 4.85 N, find the size of the contact force between the two blocks.
If instead an equal but oppositely directed force is applied to M1 rather than M2, find the size of the contact force between the two blocks.
To find the size of the contact force between the two blocks when a horizontal force F is applied to M2, we need to consider the following:
1. Draw a free-body diagram for each block:
- For M1: It only experiences the force of contact from M2 in the left direction.
- For M2: It experiences the force of contact from M1 in the right direction and also the applied force F.
2. Use Newton's second law (F = ma) to analyze the forces acting on each block in the horizontal direction:
- For M1: The contact force from M2 creates the acceleration of M1. Therefore, F_contact = M1 * a.
- For M2: The applied force F and the contact force from M1 result in the acceleration of M2. So, F - F_contact = M2 * a.
3. Since the blocks are in contact on a frictionless table, their accelerations must be the same. Therefore, we can equate their accelerations (a1 = a2 = a).
4. Now, we can combine the equations from step 2 and simplify:
- F - (M1 * a) = M2 * a.
- Rearrange the equation: (F / (M1 + M2)) = a.
- Substitute the value of F, M1, and M2 into the equation and solve for a.
5. Once we have the value of acceleration (a), we can substitute it back into one of the earlier equations to find the contact force:
- F_contact = M1 * a.
To find the size of the contact force between the two blocks when an equal but oppositely directed force is applied to M1, we follow the same steps as above, but we start by drawing the free-body diagrams considering the new force applied to M1 and the opposite directions of forces on each block.