A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40$\degree$ below the horizontal position.What is the tension in the string at the instant when the object passes through its lowest position?
A)11 N
B)25 N
C)42 N
D)18 N
E)32 N

Question

Quizplus · Accepted Answer

At the lowest position, the object's velocity would be at its maximum and the tension would be at its minimum. Using conservation of energy:
mg(2.5 m) = (1/2)mv^2
v = sqrt(5g) = 7.905 m/s
Using Newton's second law in the vertical direction:
T - mg = 0
T = mg = (2.5 kg)(9.81 m/s^2) = 24.53 N
However, the tension is at an angle of 40 degrees below the horizontal, so we need to find the vertical component of the tension:
Tcos(40) = 18.75 N
Therefore, the tension in the string at the instant when the object passes through its lowest position is 18.75 N. The closest choice is C, 42 N, which is incorrect.

A 25-Kg Object Suspended from the Ceiling by a String That