Question

Two objects with masses of 3.20 kg and 8.00 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. (a) Determine the tension in the string. (Enter the magnitude only.) N (b) Determine the acceleration of each object. (Enter the magnitude only.) m/s2 (c) Determine the distance each object will move in the first second of motion if both objects start from rest. m

Answer 1

First, write a force balance on the 3.2kg 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

(3.2kg)*a = T - (3.2kg)(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:

(3.2kg + 8kg)*a = (-3.2kg + 8kg)*(9.8m/s^2)

a= (-3.2kg + 8kg)*(9.8m/s^2)/(3.2kg+8kg) = 4.2 m/s^2 (upward for 3.2kg block and downward for 8 kg block)

That is the answer to part b)

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

T = (3.2kg)*(4.2m/s^2) + (3.2kg)(9.8m/s^2) = 44.8N

This is the answer to part a)

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

d = 1/2*a*t^2

= (0.5)*(4.2m/s^2)*(1 s)^2 = 2.1m (upward for 3.2kg block, downward for 8kg block)