The block of mass m = 1.60 kg slides along the horizontal rough plane as shown in the figure. The position coordinate x is measured from the undeformed position of the ideal spring, which has a stiffness of k = 30 N/m. At x = 0 the block is initially moving to the right with speed vi = 6 m/s. it H.= 0.30 H.= 0.20 Which of the following most nearly gives the value of

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A block with mass 300 g is held at rest against a spring with spring con- stant 200 N/m that has been compressed 3 cm from its equilibrium length. The block is released and allowed to slide on a table, and the coefficient of kinetic friction between the block and the Problem 1 table is 0.3. The block slides a short distance on the table and then comes to rest. Assume the block loses contact with the spring when the spring is at its equilibrium length, and that the friction force only acts after the block has lost contact with the spring. (a) How much work does the spring force do on the block? (b) How much work does the kinetic friction force do on the block? (c) After leaving the spring, what distance does the block slide before coming to rest? (d) What speed did the block have after sliding 5 cm from the point it lost contact with the spring?

Two blocks, m1 = 9 kg and m2 = 15 kg, are connected by a light string that passes over a frictionless pulley as shown in the figure. The first block lies on a horizontal surface and is connected to a spring with 45 N/m force constant. The system is released from rest when the spring is at equilibrium (unstretched). If the kinetic friction between m1 and the surface is 0.20, calculate: (a) the distance h which the hanging block falls before coming to rest. (b) the work done by the spring on m1  (c) the work done by the string on m1

Consider the double pendulum shown on figure below. A double pendulum is formed by attaching a pendulum directly to another one. Each pendulum consists of a bob connected to a massless rigid rod which is only allowed to move along a vertical plane. The pivot of the first pendulum is fixed to a point OO. All motion is frictionless. x2 m

A horizontal spring with stiffness 0.8 N/m has a relaxed length of 16 cm (0.16 m). A mass of 22 grams (0.022 kg) is attached and you stretch the spring to a total length of 29 cm (0.29 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns to its relaxed length of 16 cm (0.16 m)? m/s

A block of mass 1.6 kg is held against a horizontal spring so that the spring is compressed 17 cm. The block is released and it slides across the floor a distance of 3.4 m before it stops. The coefficient of friction between the block and floor is 0.185. Find the force constant of the spring.