Question

In: Physics

8) A pendulum of mass m hangs from a support fixed to a trolley. Find the...

8) A pendulum of mass m hangs from a support fixed to a trolley. Find the direction of the string of the pendulum, i.e. its angle a with the vertical, and its tension T in the following cases:
a. The trolley moves uniformly on a horizontal plane.
b. The trolley moves horizontally with acceleration a.
c. The trolley rolls freely down an inclined plane at an angle φ to the
horizontal.
d. The trolley rolls up the plane with acceleration b directed along the plane.
e. The trolley rolls down the plane with the same acceleration b.

Solutions

Expert Solution


Related Solutions

A simple pendulum with mass m = 1.6 kg and length L = 2.79 m hangs...
A simple pendulum with mass m = 1.6 kg and length L = 2.79 m hangs from the ceiling. It is pulled back to an small angle of θ = 10.7° from the vertical and released at t = 0. A)What is the period of oscillation? B)What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? C)What is the maximum speed of the pendulum? D)What is the angular displacement at t = 3.62...
A simple pendulum with mass m = 2.3 kg and length L = 2.67 m hangs...
A simple pendulum with mass m = 2.3 kg and length L = 2.67 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.4° from the vertical and released at t = 0. What is the maximum speed of the pendulum? 4) What is the angular displacement at t = 3.57 s? (give the answer as a negative angle if the angle is to the left of the vertical) 5) What is the...
A simple pendulum with mass m = 1.3 kg and length L = 2.62 m hangs...
A simple pendulum with mass m = 1.3 kg and length L = 2.62 m hangs from the ceiling. It is pulled back to an small angle of ? = 11.6° from the vertical and released at t = 0. What is the period of oscillation? What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? What is the maximum speed of the pendulum? What is the angular displacement at t = 3.67...
A simple pendulum with mass m = 1.5 kg and length L = 2.49 m hangs...
A simple pendulum with mass m = 1.5 kg and length L = 2.49 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.5° from the vertical and released at t = 0. What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? What is the maximum speed of the pendulum? What is the angular displacement at t = 3.67 s? (give the answer as a...
Consider a pendulum consisting of a mass m in a gravitational field, with the (massless) pendulum...
Consider a pendulum consisting of a mass m in a gravitational field, with the (massless) pendulum arm being a spring of spring constant k and “resting length” b. The pendulum is confined to move in a plane as usual. Write the Lagrangian and find the equations of motion.
(1 point) A brick of mass 8 kg hangs from the end of a spring. When...
(1 point) A brick of mass 8 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3920 cm. The spring is then stretched an additional 2 cm and released with a downward force of F(t)=143cos(6t) NF(t)=143cos⁡(6t) N acts on it. Assume there is no air resistance. Note that the acceleration due to gravity, gg, is g=980g=980 cm/s22. Find the spring constant  N/cm Set up a differential equation that describes this system....
A pendulum is made of 75g mass connected to a 0.88 m strong, hanging from a...
A pendulum is made of 75g mass connected to a 0.88 m strong, hanging from a support. The mass is pulled back 12 cm and released. A) what is the position of the mass 30 seconds after it is released? B) what is the maximum speed of mass?
A torsion pendulum is made from a disk of mass m = 6.6 kg and radius...
A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium 1)What is the torsion constant of this pendulum? 2)What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? 3)What is the angular frequency of oscillation of this torsion pendulum? 4)Which of 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?
A hollow sphere of mass M and radius R is hit by a pendulum of mass...
A hollow sphere of mass M and radius R is hit by a pendulum of mass m and length L that is raised at an angle θ. After the collision the pendulum comes to a stop and the sphere rolls forward into a spring with stiffness k on an incline of ϕ. Find an expression for how far ∆x the spring compresses along the incline. Use only m, L, M, R, θ, ϕ, k and appropriate constants.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT