Question

Two objects are connected by a light string that passes over a frictionless pulley as shown in the figure below. Assume the incline is frictionless and take m₁ = 2.00 kg, m₂ = 7.90 kg, and ? = 55.5

Answer 1

Given the diagram I will assume the 7.5 kg mass is on the incline; if that is incorrect, follow the same reasoning provided here

find the forces acting on each object; for m1, there is tension up and weight down, so newton's second law becomes

T - m1 g = m 1 a (assume m1 moves up and m2 moves down the plane)

for m2, the forces are T up the plane and the component of gravity down the plane

T - m2 g sin(theta) = - m2 a

Subtract equations:

m2 g sin(theta) - m1 g = m1 a + m2 a

or a = g(m2 sin(theta) - m1)/(m1+m2)

substitute values and solve for a (I get 4.5m/s/s)

knowing a, substitute this value of a in either equation to find T (28.7N)

starting from rest, v= at = 4.5m/s/s*1s