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- Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure below. The object of mass m₁ = 5.20 kg is released from rest at a height h = 2.60 m above the table. m2 (a) Using the isolated system model, determine the speed of the object of mass m₂ = 3.00 kg just as the 5.20-kg object hits the table. m/s (b) Find the maximum height above the table to which the 3.00-kg object rises. m(a) A car of weight 600 N is at rest. Another car of weight 420 N body moving to the left with a velocity of 12 m/s collides with the car which is at rest . After impact the car which is moving before impact comes to rest. Find the final velocity of body after impact and the coefficient of restitution. (b)A vehicle of mass 13 tonnes runs into a buffer stop having three buffer springs connected in parallel each of 1150 kN/cm, 2850 kN/cm and 1350 kN/cm stiffness respectively. Find the maximum compression of the springs, if the truck is travelling at 65 km/hr. Also calculate the load acting on the spring.A body of weight 370 N body moving to the left with a velocity of 14 m/s collides with another body of weight 690 N body which is at rest. After impact the body which is moving before impact comes to rest. Find the final velocity of body after impact and the coefficient of restitution The final velocity of body after impact in m/s is The coefficient of restitution is
- (a) A force of 50 N inclined at an angle of 300 with the vertical axis moves a square block of mass 6 kg that is initially at rest on a horizontal table. The force is applied with an inextensible rope attached at the top right corner of the block. Find the velocity of the block after 8 secs. Take coefficient of kinetic friction as 0.2.Two blocks A and B with masses mA = 10 kg and mB = 4 kg are connected by an inextensible cable and released from rest shown in Figure 1 (where block A is placed in position C). The cocfficients of kinetic friction between two blocks and the 30° inclined plane are uA = 0.1 and MB = 0.3. The cable is in tension in the entire motion and the sizes of blocks are negligible. (Take gravitational acceleration as 10 m/s2) - Draw separate free body diagrams of blocks A and B. Indicate clearly all the forces, directions of motion and coordinate systems. Based on the free body diagrams in part (a), cstablish the cquations of motion for blocks A and B and determine the tension in the cable between two blocks. Detemine the time required for block A to move 2.5 m from positions C to D along the incline and the velocity of block A when it reaches position D. B 2.5 m A-03 0-30° Figure ITo apply Newton’s second law and the theorem of conservation of energy to solve kinetic problems. A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has lengthL when unstretched, will first straighten and then stretch as the jumper falls.Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. Use g for the magnitude of the acceleration due to gravity. How far below the bridge, d, will the jumper eventually be hanging, once the jumper stops oscillating and comes finally to rest? Assume that the jumper does not touch the water. Express your answer in…
- A static object at an altitude of 30 m from the surface of the ground has a potential energy of 1470 J as shown in Fig. (2). If the body falls down, neglecting the air resistance, calculate: 1) The kinetic energy of the body and its potential energy at a height 20 m from the ground surface. 2) The velocity of the body at the moment of collision with the ground. KE = ? PE = ? h = 30 m h = 20 m v = ? Ground surface3. A box of mass m=15 kg at the packaging section of a factory comes to the top of a ramp (0=37°) with speed vo and slides down where it is picked up for shipment. In order to avoid damage to the box a spring is used with force constant k=100N/m and the maximum force Fmax=100N. The box slides a distance of l=4 m down the incline before it hits the spring is 0.75. as shown. The coefficient of kinetic friction between the box and entire ramp a) Find the work done by the gravity , normal force and friction force on the box until it hits the spring. b) Find the maximum speed of the box at the top of the ramp if the box is to be picked up spring is maximum compression. when the in wwwWhen Crates A and B of mass ma = 31 kg and mB = 78 kg are released from rest, Crate A moves to the right on a rough surface (u = 0.4 ). The force P = 20 Newtons is always acting on Crate B. The linear spring has a stiffness of k = 490 N and is initially stretched 0.4 meters before the system is released from rest. Neglect the mass of the pulleys and cables and neglect friction in the pulley bearings. Determine the work done by the weight of Crate B (in Joules) when Crate A has moved a distance of 0.8 meters to the right. Consider g = 10 m. 82 B
- 4) A toy wood block of mass m1= 3.25 kg is pushed by hand to compress a spring with a spring constant k= 550 N/m a distance As = 25cm. The toy block is released by the hand and the spring launches the toy block across a frictionless surface toward a more massive wood block ofimass m2= 5.0 kg. The 3.5 kg wood block is moving with an unkown velocity right before it collides with the more massive wood block which is at rest. After the collision, the 5.0 kg block is moving to the right with a velocity of 3 m/s. The more massive 5.0 kg block encounters a long rough section of surface having a coefficient of kinetic uk=0.22 and is eventually brought to rest. a) Find the velocity of the 3.25 kg block just before the collision. b) Find the velocity of the 3.25 kg block just after the collision c) What is the system's energy just before the collision? d) What is the system's energy just after the collision? e) Is this collision, elastic, completely inelastic, or inelastic? f) What is the…4. A mass mı, with initial velocity vo, strikes a mass-spring system m2, initially at rest but able to recoil. The spring is massless with spring constant . There is no friction. What is the maximum compression of the spring? k m2 m1 Vockdown New Tab A block of mass m1 = 1.23 kg on a plane inclined (h =7.85 m, and 0 = 15.7°). moving up (from rest) by a force P = 23.24 N (0 = 15.7°); mị is connected by a massless cord that is wrapped around a uniform sphere of mass M = 12.56 kg and radius R = 25.12 cm to a second block of mass m²= 0.79 kg as shown in the figure below. The coefficient of kinetic friction between m,and the surface is Hk = 0.21. Find (a) The magnitude of the acceleration for the blocks. (b) The tension T¡ in the cord at the left. (c) The tension Tz in the cord at the right. (d) The work done by the net force on m¡ when m¡reaches the top of the inclined. 1. T1