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, we can use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's analyze the first scenario where a horizontal force F is applied to M2. In this case, M2 will experience an acceleration in the direction of the force, and M1 will be at rest since it is not experiencing any external force. Since the table is frictionless, there is no friction between the blocks.
Step 1: Calculate the acceleration of M2.
To calculate the acceleration of M2, we can use the formula: F = M2 * a, where F is the applied force and a is the acceleration.
Substituting the given values, we have: 4.85 N = 3.80 kg * a.
Solving for a, we find: a = 1.28 m/s².
Step 2: Determine the contact force.
Since M1 and M2 are in contact, they will have the same acceleration. Therefore, the contact force (N) between the two blocks can be calculated using the formula: N = M1 * a.
Substituting the given values, we have: N = 1.06 kg * 1.28 m/s².
Calculating the result, we find: N ≈ 1.36 N.
In the second scenario, where an equal but oppositely directed force is applied to M1, the same steps can be followed to determine the contact force between the two blocks. Since the masses remain the same, the contact force will have the same magnitude.
Thus, the size of the contact force between the two blocks in both scenarios is approximately 1.36 Newtons.