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 in the given scenario, we need to understand Newton's third law of motion which states that for every action, there is an equal and opposite reaction.
First, let's consider the scenario where the force F is applied to M2. In this case, since the surface is frictionless, the force is transmitted equally between the two blocks.
To find the contact force, we can use the equation:
F = m1 * a1 = m2 * a2
Where F is the applied force (4.85 N), m1 is the mass of M1 (1.06 kg), m2 is the mass of M2 (3.80 kg), and a1 and a2 are the acceleration of M1 and M2, respectively.
Since the blocks are in contact, they will move together with the same acceleration. Therefore, a1 = a2 = a.
We can rearrange the equation to solve for a:
a = F / (m1 + m2)
Substituting the given values, we have:
a = 4.85 N / (1.06 kg + 3.80 kg) = 1.00 m/s^2
Now that we have the acceleration, we can find the contact force by multiplying the mass of M1 with the acceleration:
Contact force = m1 * a = 1.06 kg * 1.00 m/s^2 = 1.06 N
Therefore, in the first scenario, the size of the contact force between the two blocks is 1.06 N.
Now let's consider the scenario where an equal but oppositely directed force is applied to M1 rather than M2.
Following the same approach, we can calculate the acceleration of the blocks as:
a = F / (m1 + m2) = 4.85 N / (1.06 kg + 3.80 kg) = 1.00 m/s^2
Using this acceleration, we can find the contact force again:
Contact force = m1 * a = 1.06 kg * 1.00 m/s^2 = 1.06 N
Hence, in the second scenario as well, the size of the contact force between the two blocks is 1.06 N.