Question

In: Physics

A simple pendulum consists of a 3.0kg mass attached to a 5.0m long light rope. The...

A simple pendulum consists of a 3.0kg mass attached to a 5.0m long light rope. The upper end of the rope is fixed on the ceiling of the lecture theatre. At time t = 0s the rope holding the mass makes an angle 0.040rad to the left of its equilibrium position moving to the right at 0.056rad/s .

a) What is the maximum angle the rope makes with the vertical? answer = 0.057rad

b) When is the first time after t = 0.0s when the rope makes an angle θ = 0? answer = 0.56s

c) What is the time rate of change of θ (ie d/dtθ) at 2.3s? answer = −0.061rad/s

Please post detailed solutions. The answers are included. Thank you.

Solutions

Expert Solution


Related Solutions

A simple pendulum consists of a particle of mass m suspended by a long, massless wire...
A simple pendulum consists of a particle of mass m suspended by a long, massless wire of length L. Draw a free body diagram for the pendulum bob corresponding to a moment when the bob is located an angular displacement Φ away from (eg. to the right of) equilibrium. Determine an expression in terms of m, g, and Φ for the component of the net force on the bob that points tangent to the path of the bob. Assume that...
Two blocks with different mass are attached to either end of a light rope that passes...
Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.20m , its speed is 1.50m/s . a. If the total mass of the two blocks is 16.0kg , what is the mass of the more massive block? Take free fall acceleration...
A simple pendulum consists of a small object of mass m= 0.150 kg suspended from a...
A simple pendulum consists of a small object of mass m= 0.150 kg suspended from a support stand by a light string. The string has a length L= 0.750 m. The string has an initial position given by θ= 65.0° relative to the vertical. The pendulum is released from rest. Air resistance is negligible during the subsequent motion of the pendulum. a)Calculate the work done by gravity on the pendulum as it moves from its initial position to the lowest...
1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a...
1. A simple harmonic oscillator consists of a block of mass 4.20 kg attached to a spring of spring constant 290 N/m. When t = 2.10 s, the position and velocity of the block are x = 0.141 m and v = 3.530 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? 2. If you took your pendulum to the moon, where the acceleration...
A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring...
A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring of spring constant 260 N/m. When t = 1.60 s, the position and velocity of the block are x = 0.199 m and v = 3.920 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 3.4 kg attached to a spring...
A simple harmonic oscillator consists of a block of mass 3.4 kg attached to a spring of spring constant 120 N/m. When t = 0.84 s, the position and velocity of the block are x = 0.127 m and v = 3.23 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
Block A rests on a horizontal tabletop. A light horizontal rope is attached to it and...
Block A rests on a horizontal tabletop. A light horizontal rope is attached to it and passes over a pulley, and block B is suspended from the free end of the rope. The light rope that connects the two blocks does not slip over the surface of the pulley (radius 0.080 m) because the pulley rotates on a frictionless axle. The horizontal surface on which block A (mass 3.30 kg) moves is frictionless. The system is released from rest, and...
As in the figure below, a simple harmonic oscillator is attached to a rope of linear...
As in the figure below, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 ✕ 10−2 kg/m, creating a standing transverse wave. There is a 3.5-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.1 rad/s and an amplitude of 255.0 cm. (a) What is the distance between adjacent nodes? m (b) If the angular frequency of the oscillator doubles, what happens to the...
There are two correct answers for this question: A simple pendulum and a spring-mass pendulum both...
There are two correct answers for this question: A simple pendulum and a spring-mass pendulum both have identical frequencies. Which changes will result in the spring-mass system having twice the period of the pendulum? a) Quadruple the mass of the simple pendulum b) Replace the spring with one half the spring constant and double the mass c) Make the string on the pendulum four times smaller and make the pendulum 4 times more massives d) Double the mass in the...
Q1: Consider the simple pendulum system, the length of the pendulum is ‘l’ and mass ‘m’...
Q1: Consider the simple pendulum system, the length of the pendulum is ‘l’ and mass ‘m’ has simple harmonic motion. Find the equation of motion using 2 approaches: Newtonian and Lagrangian. What do you conclude?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT