How Does Force Distribution Affect Two Blocks on a Frictionless Table?

[physics newb]

OK, this should be my last question. Again, I need an answer soon, but I'm also here to learn.

Two Blocks are in contact on a frictionless table, one larger than the other. A horizontal force is applied to the larger block, pushing against the smaller block. (a) If m_A = 2.3 kg (the larger block), m_B = 1.2 kg (the smaller block), and F = 3.2 N, find the magnitude of the force between the two blocks. (b) Show that if a force of the same magnitude F is applied to the smaller block but in the opposite direction, the magnitude of the force between the blocks is 2.1 N, which is not the same value calculated in (a). (c) Explain the difference. I'm not quite sure what to do with the information given, so again, any help would be great!

 

[Astronuc]

One has enough information.

Since the blocks are in contact, the applied for F acts on the mass of both (both must be accelerating), BUT, the force acting on (transmitted to) the larger block by the smaller block is less than the force that the larger block would apply to the smaller block - because . . . (what does mass do?)

Think F = ma.

 

[Architeuthis Dux]

(a) To find the magnitude of the force between the two blocks, we can use Newton's Second Law, which states that force is equal to mass times acceleration (F=ma). In this case, the acceleration of the blocks will be the same since they are in contact and on a frictionless surface. Therefore, we can set up the following equation: F = (m_A + m_B)a. Rearranging for a, we get a = F/(m_A + m_B). Plugging in the given values, we get a = 3.2 N/(2.3 kg + 1.2 kg) = 1 m/s^2. Now, using this acceleration value, we can find the force between the blocks by using F = ma again. So, the magnitude of the force between the two blocks is F = (m_B)a = (1.2 kg)(1 m/s^2) = 1.2 N.

(b) In this case, the force is applied to the smaller block in the opposite direction. This means that the smaller block will accelerate in the opposite direction, while the larger block will still accelerate in the original direction. This results in a net force between the blocks that is equal to the difference of the two individual forces, which is 3.2 N - 1.2 N = 2 N. However, this is not the same as the force calculated in part (a) because the two blocks have different accelerations and therefore the force between them will be different.

(c) The difference in the magnitude of the force between the blocks is due to the difference in their masses and accelerations. In part (a), the larger block has a greater mass, so it requires a greater force to accelerate it at the same rate as the smaller block. In part (b), the force is being applied to the smaller block, so it will experience a greater acceleration and therefore a greater force between the blocks. This highlights the importance of considering all factors, such as mass and acceleration, when calculating forces in a system.