A pendulum consists of a string of length L and a mass m hung at one end and the mass oscillates along a circular arc. Part a) Familiarize yourself with the derivation of omega = Squareroot g/L to hold. i) Explain succinctly how the angular frequency of oscillation omega = Squareroot g/L comes about from Newton's Law, where g is the gravitational acceleration. ii) One assumption required is the small angle approximation: sin theta = theta and cos theta =...
This mass (m) on a string (of length L) is moving in a horizontal circle. The string makes an angle of 60 degrees with the vertical. (Express your answers in terms of m, L, g, and theta) Find the tension in the string. Find the speed of the mass.
10. An object of mass m is tied to a string of length L and a variable horizontal force is applied o zero and gradually increases until the string makes an angle with the vertical. Work done by the force F is: n it which starts at A) mgl B) mgl (1-sin θ ) C) mgl (1-cos ) D) mgl (1 + sin θ ) E) mgL cos6
A mass m = 4.700 kg is suspended from a string of length L = 1.270 m. It revolves in a horizontal circle. The tangential speed of the mass is 2.243 m/s. What is the angle theta between the string and the vertical (in degrees)?
A mass m = 4.300 kg is suspended from a string of length L = 1.290 m. It revolves in a horizontal circle (see Figure). The tangential speed of the mass is 3.743 m/s. What is the angle theta between the string and the vertical (in degrees)?
A vertical spring has a length of 0.175 m when a 0.225 kg mass hangs from it, and a length of 0.775 m when a 1.85 kg mass hangs from it. What is the force constant of the spring, in newtons per meter? What is the unloaded length of the spring, in centimeters?
A mass M = 4 kg attached to a string of length L = 2.0 m swings in a horizontal circle with a speed V. The string maintains a constant angle theta θ= 46.5 degrees with the vertical line through the pivot point as it swings. What is the speed V required to make this motion possible?
The figures to the right show a rod with length, \(l\), and mass, \(M\), on a frictionless table rotated an angle \(\theta\) from the horizontal. It is fix to the table by a pin through its center of mass, and can rotate freely about this pin. On the two ends of the rod are connected identical springs with spring constant, \(k\), and the equilibrium position of the springs is when \(\theta=0\). In this problem, \(\theta \ll 1 \mathrm{rad}\), and the...
2. [2pt] A mass m = 9.100 kg is suspended from a string of length L = 1.210 m. It revolves in a horizontal circle (see Figure). The tangential speed of the mass is 3.089 m/s. What is the angle theta between the string and the vertical (in degrees)? Answer: Submit All Answers
A 5.61-kg ball hangs from the top of a vertical pole by a 2.43-m-long string. The ball is struck, causing it to revolve around the pole at a speed of 4.17 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole. Take g = 9.81 m/s2. What is the tension of the string?