Question

What is the acceleration of two connected blocks on a frictionless table when a 10 N force is applied to one of the blocks, given that one block has a mass of 2 kg and the other block has a mass of 3 kg?

Answer 1

To find the acceleration of the two connected blocks on a frictionless table when a force is applied, we can use Newton's second law of motion.

1. **Identify the total mass**:
The two blocks have masses:
- \( m_1 = 2 \, \text{kg} \) (first block)
- \( m_2 = 3 \, \text{kg} \) (second block)

The total mass \( M \) of the system is:
\[
M = m_1 + m_2 = 2 \, \text{kg} + 3 \, \text{kg} = 5 \, \text{kg}
\]

2. **Apply the net force**:
A force \( F = 10 \, \text{N} \) is applied to the system. Since it's a frictionless table, this force is the only force acting horizontally, and it will cause both blocks to accelerate together.

3. **Newton's second law**:
According to Newton's second law:
\[
F = M \cdot a
\]
Rearranging for acceleration \( a \):
\[
a = \frac{F}{M}
\]

4. **Calculate the acceleration**:
Substitute the values for \( F \) and \( M \):
\[
a = \frac{10 \, \text{N}}{5 \, \text{kg}} = 2 \, \text{m/s}^2
\]

Thus, the acceleration of the two connected blocks is \( \boxed{2 \, \text{m/s}^2} \).