Question

Calculate the acceleration of the two masses shown in the picture above.

A. 0.77 m/s^2
B. 3.92 m/s^2
C. 8.62 m/s^2
D. 5.91 m/s^2

Answer 1

Hello!

We can begin by summing the forces acting on each mass. (Tension is CONSTANT because the string is both frictionless and massless).

On the 3 kg block: (Ignore forces acting in the vertical direction since there is no motion in that axis)

∑F = -M₁gsinФ + T

On the 8 kg block:

∑F = -T + M₂g

Sum the forces:

∑F = -M₁gsinФ + T -T + M₂g

∑F = -M₁gsinФ + M₂g

Divide by both masses to get the acceleration:

`a = (-M_1gsinФ + M_2g)/(m_1+m_2)`

Plug in values: (g = 10m/s²)

`a = (-(3)(10)(sin30)+8(10))/(3+8) = 5.91 m/s^2`