# Newtons Laws of Motion Problem

**1. The problem statement, all variables and given/known data**

Mass of Block A = 1 kg

Mass of Wedge B = 2 kg

Inclination of Wedge is 37°

and Cos 37° = 4/5

The wedge is given an acceleration of 5 ms

^{-2}

Find –

1. Acceleration of Block wrt Wedge

2. Normal Force

**2. Relevant equations**

Newton’s Law for a System (hereby referred as NLS)

∑f_{ext} = m_{1}a_{1}+m_{2}a_{2}……+m_{n}a_{n}

**3. The attempt at a solution**

Let the Acceleration of Block wrt Wedge be λ along the inclination.

In Y axis, there is only one Ext force i.e. The gravity and ∑f_{net} in Y direction is m_{1}g+ m_{2}g = (m_{1}+ m_{2})g

Therefore in Y axis using Newton’s Law for a System,

m_{A}a_{A} + m_{B}a_{B} = (m_{1}+ m_{2})g

but in Y axis , a_{A} = 0

and a_{b} in Y axis = λsinθ + a_{A}cos 90

= λsinθ + 0

= λsinθ

Therefore, m_{B}a_{B} = (m_{1}+ m_{2})g

1 (λsin(θ)) = (1 + 2)g

λ sin 37° = (3)10

λ(3/5) = 30

λ = 50

but using pseudo force, λ = 2 ms^{-2} which is correct answer in the Answer Key

Where am I going Wrong?

Please Help

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