Question

Two objects with masses of m_1 = 2.00 kg and m_2 = 8.00 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. Determine the tension in the string. (Enter the magnitude only.) Determine the acceleration of each object. (Enter the magnitude only.) Determine the distance each object will move in the first second of motion if both objects start from rest.

Answer 1

Given masses,

m1 = 2kg

m2 =8 kg

First, write a force balance on the 2kg object:

The forces are gravity Fg (downward) and tension T (upward), and the object is moving from the problem statement:

m*a = T - mg , or

(2kg)*a = T - (2kg)(9.8m/s^2)

Do the same for the 8 kg object:

m*a = T - mg, or

(8kg)*a = T - (8kg)*(9.8m/s^2)

Since the two blocks are connected via a taut string, a is the same (in magnitude) for both but opposite in sign. We can subtract the two equations to eliminate T from the equations and solve for a:

(2kg + 8kg)*a = (-2kg + 8kg)*(9.8m/s^2)

a= (-2kg + 8kg)*(9.8m/s^2)/(10kg) = 5.886 m/s^2 (PART-B ANSWER) (upward for 2kg block and downward for 8 kg block)

You can substitute this back into the first equation to solve for T:

T = (2kg)*(5.886m/s^2) + (2kg)(9.8m/s^2) = 31.392 N

TENSION IN THE STRING = 31.392 N (PART-A ANSWER)

For part c) you can use the equation of motion:

d = 1/2*a*t^2

= (0.5)*(5.886m/s^2)*(1 s)^2 = 2.943 m (PART-C ANSWER) (upward for 2kg block, downward for 8kg block)