An object of mass m is connected to a light spring with a force constant of...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
A 0.53 kg object connected to a light spring with a force constant of 23.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. _____________cm/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. ___________ cm/s (c) Determine the speed of the object when the spring is stretched 1.5 cm. _______________cm/s (d) For what value of x does...
3. The rigid uniform pendulum of mass m is initially at rest at 0 0. Using Newton's 2nd law, derive the equation of motion and solve for 0 as a function of time. Include the effect of gravity. Assume the rotation is small. Show all work. a k b C Focos(wt) Act Go to 3. The rigid uniform pendulum of mass m is initially at rest at 0 0. Using Newton's 2nd law, derive the equation of motion and solve...
a ball with mass of 8.00kg... 2. A ball with mass of 8.00 kg is thrown downward with a speed of 15.0 m/s. When it has dropped 10.0 m, its speed is 18.0 m/s. While falling, the ball has an upward, constant drag force of unknown magnitude D. What is D? Ans: 38.9 N 3. A 2.00 kg object is attached to a Hooke's Law spring with k = 250 N/m. When the spring is compressed by 16.0 cm, the...
A 0.52-kg object connected to a light spring with a force constant of 19.4 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (a) Determine the maximum speed of the object. Correct: Your answer is correct. m/s (b) Determine the speed of the object when the spring is compressed 1.5 cm. Correct: Your answer is correct. m/s (c) Determine the speed of the object as it passes the point 1.5 cm from...
A 0.56-kg object connected to a light spring with a force constant of 23.6 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest. (d) For what value of x does the speed equal one-half the maximum speed? m
A 300-g object is attached to a spring that has a force constant of 80 N/m. The object is pulled 8 cm to the right of equilibrium and released from rest to slide on a horizontal frictionless table. (a) Calculate the maximum speed of the object. An object (m0.300 kg) attached to a spring (k 80 N/m) is pulled A 0.08 m to the right of equilibrium and released from rest. It begins to oscillate on a horizontal, frictionless table....
A 1.00 kg glider attached to a spring with a force constant 25.0 N/m oscillates on a horizontal, frictionless air track. At t = 0, the glider is released from rest at x = -2.70 cm. (That is, the spring is compressed by 2.70 cm.) (a) Find the period of its motion. s (b) Find the maximum values of its speed and acceleration. m/s m/s2 (c) Find the position, velocity, and acceleration as functions of time (t). x(t) = cm...
Hi, can you solve the question for me step by step, I will rate up if the working is correct. I will post the answer together with the question. Answer: Question 5 A particle of mass m rests on a smooth horizontal track. It is connected by two springs to fixed points at A and B, which are a distance 2lo apart as shown in Figure Q5. The left-hand spring has natural length 2lo and stiffness k, whilst the right-hand...
Consider two masses, both with mass M, attached to a spring with spring constant k. They slide along angled rails, and the angle between the rails is theta. There is no friction: the masses slide freely along the rails. Assume that the masses move together so that the spring remains parallel to its equilibrium position. The masses are initially moving upwards such that the spring is being stretched past its equilibrium length. Describe what happens next, by using Newton's second...