Question

Two objects are connected by a massless string going over a frictionless, massless pulley, as shown. Object 1 is 4.0 kg and object 2 is 6.0 kg.

a) For each object, draw a free-body diagram showing all forces, the presumed direction of acceleration (if any), and an appropriate choice of x−y axes.
b) If necessary, break one or more of the forces into appropriate x \& y components.
c) Apply Newton's Second Law to the free body diagrams, write equations relating the forces, masses, and accelerations, as taught in this unit. d) Solve the relevant equations to find the accelerations of the two objects.

Answer 1

(a) The free body diagram of the forces acting on the objects consist of weight of the objects, and normal force acting upwards.

(b) The forces acting on the objects in vertical direction include the normal force and weight of the objects.

(c) The equation for the net force acting on the objects is m₁g - m₂g = (m₁ + m₂)a

(d) The acceleration of the two objects is 1.96 m/s².

How to draw the free body diagram of the forces acting on the objects?

(a) The free body diagram of the forces acting on the objects consist of weight of the objects, and normal force acting upwards.

(b) The forces acting on the objects in vertical direction include the normal force and weight of the objects.

(c) The equation for the net force acting on the objects is given as;

F(net) = ma

m₁g - m₂g = (m₁ + m₂)a

(d) The acceleration of the two objects is calculated as follows;

m₁g - m₂g = (m₁ + m₂)a

where;

• m₁ is the 6 kg mass
• m₂ is the 4 kg mass
• g is acceleration due to gravity
• a is the acceleration of the objects

(6 kg x 9.8 m/s²) - ( 4 kg x 9.8 m/s²) = (6 kg + 4 kg ) a

19.6 = 10a

a = 19.6 / 10

a = 1.96 m/s²