Question

Two blocks of mass \( 20\,\text{kg} \) and \( 30\,\text{kg} \) are placed in contact on a smooth horizontal surface. A force \( F = 60\,\text{N} \) is applied to the \( 20\,\text{kg} \) block. Find the force exerted by the \( 20\,\text{kg} \) block on the \( 30\,\text{kg} \) block.

• A. \(12\,\text{N}\)
• B. \(24\,\text{N}\)
• C. \(30\,\text{N}\)
• D. \(36\,\text{N}\)

Hint:

To find the contact force between blocks on a frictionless surface, calculate the common acceleration first, then apply Newton's second law to the block being pushed.

Answer 1

The Correct Option is D

Step 1: Find the acceleration of the system.
Since the blocks move together on a smooth surface, they share the same acceleration: \[ \text{Total mass} = 20 + 30 = 50\,\text{kg}, \quad F = 60\,\text{N} \] \[ a = \frac{F}{m} = \frac{60}{50} = 1.2\,\text{m/s}^2 \] Step 2: Consider the force on the \(30\,\text{kg}\) block.
Let the force exerted by the \(20\,\text{kg}\) block on the \(30\,\text{kg}\) block be \(F_c\). Since the \(30\,\text{kg}\) block accelerates at \(1.2\,\text{m/s}^2\), \[ F_c = m \cdot a = 30 \cdot 1.2 = 36\,\text{N} \]