A simple pendulum with mass m = 1.4 kg and length L = 2.27 m hangs from the ceil

Question

A simple pendulum with mass m = 1.4 kg and length L = 2.27 m hangs from the ceiling. It is pulled back to an small angle of = 8.6° from the vertical and released at t = 0. 1) What is the period of oscillation? s Submit Help You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N Submit Help You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s Submit Help You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 4) What is the angular displacement at t = 3.45 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° Submit Help You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 Submit You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 Submit You currently have 0 submissions for this question. Only 6 submission are allowed. You can make 6 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward

Explanation / Answer

m = mass of the bob = 1.4 kg
L = length of the pendulum = 2.27 m
= initial angle of the pendulum = 8.6°
g = acceleration by gravity = 9.8 m/s²

1.)What is the period of oscillation?

T = 2*pi * sqrt(L/g)
T = 2*pi*sqrt(2.27/9.8)
T = 3.02 s
Time period of the Oscillation, T = 3.02 s

2.) What is the magnitude of the force on the pendulum bob perpendicular to the string ?
F = m*g* sin()
F = 1.4 * 9.8 * sin(8.6°)
F = 2.05 N

3.)
Using Conservation of energy -
PE = KE
mgh =(1/2)mv^2
v^2 = 2gh
Where h = L×(1 - cos())

v = sqrt(2*9.8*2.27 *(1 - cos(8.6)))
v = 0.707 m/s

4.) What is the angular displacement at t = 3.45 s ?
= 2/(3.02) = 2.08 rad/s

= 8.6º * cos(2.08 t)
= 8.6º * cos(2.08 *3.45 )
= 5.4º

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.