Problem 2 A flexible chain (which can be bent to fall) of length 'Q' (per unit length) is released from rest. What is the speed of the chain when it leaves the horizontal position? (Solve using conservation of energy) The chain is homogeneous
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- A particle of mass m = 1.50 kg moves along one dimension and is subject to a single force, whose potential energy function is given by U(x) = x4 – 2x2 + 4 (where U is measured in Joules and x is measured in meters). At the moment when the particle is located at position x = 1.50 m, its speed is v = 2.50 m/s. %3DTarzan, who weighs 645 N, swings from a cliff at the end of a convenient vine that is 17 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 2.5 m. The vine will break if the force on it exceeds 1050 N. What would the greatest force on the vine be during the swing? Number i Units1. A roller-coaster car with a mass of 1200 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. [Express your answers in kilojoules (kJ).] a. What is the initial potential energy of the car? b. What is the potential energy at point B? c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40 000 J (40 kJ), what is the kinetic energy of the car at point B 2. The time required for one complete cycle of a mass oscillating at the end of a spring is 0.80 s. What is the frequency of oscillation?
- A 20.0-kg child descends a slide 1.80 m high and reaches the bottom with a speed of 1.25 m/s . Part A How much thermal energy due to friction was generated in this process? Express your answer to three significant figures and include the appropriate units.#13 Work Energy TheoremA mass M with an initial velocity v0 slides across a level surface, subject to a force of friction where the coefficient of kinetic friction is μk, eventually coming to a halt. The total work done on the mass A. depends on μk B. depends on both μk and the initial speed v0 C. depends on neither μk nor the initial speed v0 D. does not depend on μk, and is given by 1/2MvA small box with mass m is released from rest by a spring compressed a 3. distance d. The spring constant is k. After being released, the object slides along a frictionless track. What is the speed of the box when it reaches point B at height h/2? What must be the value of d so that the box comes to rest at the top of the track at point C? Law B h m Application A
- Which of the following statements are true? options: The rest length of a spring is where it applies zero force. The spring constant has units of N/m. Work can be calculated for a force that depends on position. Work is the slope of the force vs. position graph. If we stretch a spring twice as far beyond the rest length, the spring force is 4x larger. If we stretch a spring twice as far beyond the rest length, the potential energy is 4x larger.A particular spring on the Earth is found to have a spring constant of k = 1400 N/m. If the same spring is taken to Marsa. The spring constant will be less than on Earthb. The spring constant will be the same as on Earthc. The spring constant will be more than on Earthd. Springs do not work on Marse. We cannot answer this question because we cannot get a spring to MarsUS-2 A spring has a force constant K=12.5N/m. a) Find the energy stored in the spring if it is stretched x₂-0.150m from its unloaded length. b) Find the energy stored in the spring if it is stretched x₁-0.300m from its unloaded length. c) Find U₁U₁, the ratio of the energies you found in parts a) and b). d) The ratio x/x₁ is 2/1. Why is this not the same as your answer for part c)?