Question

Physics question regarding acceleration of 2 boxes attached to pulley over inclined plane?

Box A (mass = 10 kg) rests on a surface inclined at 37 degrees to the horizontal. It is connected by a lightweight cord, which passes over a massless and frictionless pulley, to the second box B (mass = 11 kg).
The coefficient of kinetic and static friction are 0.300.
What are the accelerations of the boxes?

Answer 1

Let the acceleration of the system be `a` .

Considering the forces on B we can write

`m_2g-T=m_2a`

`=>T=m_2(g-a)............[1]`

Considering the forces on A we can write

`T-mum_1gcostheta-m_1gsintheta=m_1a`

`T=color(orange)(mum_1gcostheta)+color(cyan)(m_1gsintheta)+m_1a.......[2]`

Comparing [1] and [2] we get

`mum_1gcostheta+m_1gsintheta+m_1a=m_2(g-a)`

`=>(m_1+m_2)a=m_2g- mum_1gcostheta-m_1gsintheta`

`=>a=(m_2g- mum_1gcostheta-m_1gsintheta)/(m_1+m_2)`

Inserting

`g=10m"/"s^2,m_1=10kg,m_2=11kg,mu=0.3,costheta=cos37^@=0.8 and sintheta=sin37^@=0.6`

we get

`=>a=(m_2g- mum_1gcostheta-m_1gsintheta)/(m_1+m_2)`

`=>a=(11xx10- 0.3xx10xx10xx0.8-10xx10xx0.6)/(10+11)m"/"s^2`

`=>a=(110- 24-60)/21m"/"s^2`

`=>a=26/21=~~1.24m"/"s^2`