Question

Please solve for acceleration and show all steps for both M1 going up while M2 is going down, and M2 going up while M1 is going down.

a бка mi I m, = 5.0kg Team2 = 1.5kg [m2 11.5kg L o = 20.00 VA ? assume no faction

Answer 1

Let T be the tension in the string. We don't know whether the m₁ will accelerate up the incline or down the incline. In our analysis we will assume the acceleration of m₁ down the incline to be positive. However, if the acceleration turns out to be negative then the acceleration will be up the incline. Since both the masses are connected by an inextensible string, the acceleration of both the boxes will be equal.

There are three forces acting on the object of mass m₁: gravitational force of the Earth, normal force of the incline, and tension in the string.

There are two forces acting on the object of mass m₂: gravitational force of the Earth, and tension in the string.

The free-body diagram of the two masses is shown below:

дих 2 Migsind in Резьд

The gravitational force on mass m₁ is resolved into components parallel and perpendicular to the incline.

Consider the box of mass m₂. Since we have assumed the box of mass m₁ to accelerate down the inline, the box of mass m₂ will accelerate down the incline.

mga = T - m29

m2a + m2g =T

The box of mass m₁ is not allowed to move in direction normal to the inline, the net force on the box in this direction must be zero.

N1 - mig cos d = 0

The net force along the incline accelerates the block

mia = mig sin -T

Using equation (1)

mja = mig sin A - (mza + m29)

mja = mig sin 4 - m2a - m29

mja + m2a = mig sind – m29

(mı + m2 a = (mı sin – m2),

a = (my sin 0 - m2). mi + m2

Substituting values

a = ((5 kg) sin 20° – 1.5 kg) x (9.8 m/s2) 5.0 kg + 1.5 kg

a = 0.317 m/s?

The acceleration turns out to be positive, so mass m₁ will accelerate down the incline, and mass m₂ will accelerate upward.