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- Homework Statement
- Two blocks initially at rest are kept in contact as shown in the figure. A force F is applied on the left block. The blocks are of masses ##m_1## and ##m_2##. Find the acceleration of the blocks. All surfaces are smooth.

- Relevant Equations
- ##Force = Mass \times Acceleration##

**Attempt at Solution::**

##m_2## is chosen as reference frame and FBD is drawn as shown above. We get the following equations:

From ##m_1## by choosing axes along and perpendicular to acceleration of ##m_1## w.r.t ##m_2## (##a'##):

$$

m_1 a' + m_1 a \cos{\theta} + m_1 g \sin{\theta} = N_1 \sin{\theta} + F \cos{\theta}

$$

$$

N+N_1 \cos{\theta} + m_1 a \sin{\theta} = m_1 g \cos{\theta} + F \sin{\theta}

$$

From ##m_2## by choosing horizontal and vertical axes:

$$

N_2 = N \cos{\theta} + m_2 g

$$

$$

m_2 a = N \sin{\theta}

$$

Which gives us four equations, but five variables, namely ##a',a,N_1 ,N_2, N##