Question

In the following figure m_1 = 20.0kg kg and á alpha = 50.9 ∘ ^\circ. The coefficient of kinetic friction between the block and the incline is ì k = 0.40

What must be the mass m 2 of the hanging block if it is to descend 9.00m m in the first 3.00s s after the system is released from rest?

Answer 1

s=at²/2 +> a=2s/t²=
=2•910⁻³/3²=2•10⁻³ m/s².

m₁a=T-F(fr) -m₁gsinα,
0=m₁gcosα –N,
m₂a=m₂g –T.

F(fr) =μN=μm₁gcosα .

m₁a=T- μm₁gcosα -m₁gsinα,
m₂a=m₂g –T.

m₁a + m₂a= m₂g - μm₁gcosα -m₁gsinα
m₂(g-a) = m₁(a+ μgcosα+gsinα)

m₂=[m₁(a+ μgcosα+gsinα) ]/(g-a)