Answer:
The answers to the question are
(a) 2.1 m/s
(b) 0.83 N
(c) 1.9 N
Explanation:
To solve the question, we list out the varibles
Length, l of string = 0.8 m
mass of rock, m = 0.12 kg
Angle with the verrticakl, θ = 45 °
a) To find the speed of the rock when the string passes through the vertical position we have
From the first law of thermodynamics
Potential energy = kinetic energy
m×g×l×(1-cosθ) = 1/2×m×v²
That is v² = 2×g×l×(1-cosθ)
= 2×9.81×0.8×(1-cos45) = 4.597
or v = √4.597 = 2.1 m/s
(b) The tension in the string when it makes an angle of 45∘ with the vertical is given by
For balance between Tension and mass of rock is gigen by
∑Forces = 0, T - m×g×cosθ = 0
or T = m×g×cosθ = 0.12×9.81×cos45 = 0.83 N
c) The tension in the string as it passes through the vertical
when passing through the vertical we have T - m×g = (m×v²)/r
or T = m×g + (m×v²)/r = mg(1+2(1-cosθ)) =0.981*0.12 (1+ 2(1-cos45)) =1.867 N
= 1.9 N
