Question

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° 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

Answer 1

Answer: c) 42 N

Explanation:

M = 2.5 kg

L = 2.5 m

h = L(1 - sin 40 degrees)

Potential energy Mgh = MgL(1 - sin 40 degrees )

kinetic energy = MgL(1 - sin 40 degrees)

(1/2)Mv^2 = MgL(1 - sin 40 deg)

Mv^2 = 2MgL(1 - sin 40 deg)

Fc = Mv^2/L

Fc = 2Mg(1 - sin 40 deg)

= 2 x 2.5 x 9.8 x (1 - sin 40 deg)

Fc = 17.5 N

Let T = tension in the string.

T - Mg = Fc

T - 2.5 x 9.8 = 17.5

T - 24.5 = 17.5

T = 17.5 + 24.5

T = 42 N