3. A mass m (2.0 kg) is attached to a horizontal spring of spring constant k (25 N/m) which is held stretched a distance x = 0.25 m from its relaxed position by a force, and then released. The spring compresses, pulling the mass. Assume there is no friction. a. Determine the speed of the mass when the spring returns to its relaxed position. b. Determine the speed of the mass when the spring is compressed by x/2.
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- The figure shows a steel bar being processed by a rolling mill. Given that P=80kN and r =0.016, determine the force F required to advance the bar at a constant speed.The lower block of mass m2 = 3.2 kg is pulled on by a rope with a tension force of 28 N. The upper block has mass m1 = 1.8 kg. The coefficient of kinetic friction between the lower block and the surface is 0.32. The coefficient of kinetic friction between the lower block and the upper block is also 0.32. What is the acceleration of the 3.2 kg block?When Crates A and B of mass ma = 38 kg and mB = 74 kg are released from rest, Crate A moves to the right = 0.2 ). The force P = 18 Newtons is always acting on Crate B. The linear spring on a rough surface (u: has a stiffness of k = 480 N and is initially stretched 0.5 meters before the system is released from rest. m Neglect the mass of the pulleys and cables and neglect friction in the pulley bearings. Determine the work done by the external force P (in Joules) when Crate A has moved a distance of 0.5 meters to the right. wwwwm
- 3. A block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00 %3D kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied to the 2.00-kg block, setting it in motion as shown in Figure. The distance L that the leading edge of the smaller block travels on the larger block is 3.00 m. L M m M (a) Draw a separate free-body diagram for each block. (b) In what time interval will the smaller block make it to the right side of the 8.00-kg block? as (Note: Both blocks are set into motion when the force is applied.) (c) How far does the 8.00-kg block move in the process?Q1. m-1 kg m,=4 kg The mechanism set up with m,, m, and weightless pulleys is as shown in the figure. Then, the masses are released. Static and kinetic friction between the inclined plane and m, are 0.6 and 0.5 respectively. What are the accelerations of m, and m,? (g = 10 m / s². Frictions and mass of the pulley are ignored.) Q2. 300 m/s .*........ yatay 100 m/s 320 m x=? A plane is flying horizontally at an altitude of 320 m with 300 m/s speed. It launches its bomb with 100 m/s speed relative to the plane as shown. How many meters away from the castle should the plane launch its bomb to hit the castle. (g=10 m/s², sin370=0.6; cos37°=0.8) Q3. 2 kg The object in the frictionless cone in the figure is making a uniform circular motion. Calculate, a) the normal force that the cone exerts on the object, b) centripetal force applied to the body, c) Find the speed of the object.A spring of stiffness k = 500 N/m is mounted against the 10-kg block. If the block is subjected to the force of F = 500 N, The kinetic coefficient friction is 0.5. F = 500 N S 5 3 k = 500 N/m www 4 The velocity of block is ...........when stretched of spring (s) is 0.5 m. O 2.8 m/sec O4.8 m/sec O 1.8 m/sec O 3.8 m/sec
- 1. A cart is being pulled by a motor. The cart has a mass of m = 200 kg. The motor applies a horizontal force of F = 800 N to the center of the right side of the cart. The cart is 1m tall, the total length is 1.5m, the wheels are 1m apart from each other, and the center of mass G is 0.4 m above the floor and on the horizontal center. Ignore friction. If there is no rotational movement of the cart, determine the following: 1. The cart's acceleration 2. The reaction (normal) force at the front pair of wheels. 3. The reaction (normal) force at the rear pair of wheels. F 77 TI T3. 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 wwwA brake test for an automobile is conducted. During the brake test, the automobile of mass 1800 kg (including driver) is travelling at the speed of 110 km/hr as it passes point A, and the car descends a hill of 1in 2 (Sine). The driver applies brakes so as to bring the car speed at B to 50 km/hr. The total frictional resistance to motion is 235 N. Using Work-Energy Method, Calculate the following required to bring the car to 50 km/hr from 110 km/hr in 210 m (From Point A to Point B) B Determine the Value of Total Energy about Point A TE= Determine the Value of Total Energy about Point B TEb= Determine the Value of Breaking Force needed Fb= N A
- 4. A six-pound weight hanging from the end of a spring is pulled 10 centimeters below its resting position and released; it takes 0.9 seconds to complete a cycle. Determine an equation for the motion of the weight, assuming that it is 10 centimeters below its resting position and rising at t = 0. 16165 -- below t=0 t=0.93 Problem A ball of mass m is connected to a rod of length L and swings around the axis O. At some instant, the rod is at an angle and the mass has speed v. Determine the tension in the rod, T, and the rate at which the speed of the mass is increasing, v. Values: g = 9.81 m/s², 0 = 20 deg., m = 30 kg, L = 4 m, v =4 m/s. L m3. A block of mass m is connected to a spring of spring constant k and lies on a frictional road. The coefficient of friction between the road and the block is k. The spring is initially compressed by X and the spring-mass system is released from rest. The block stops after a while. Find the distance traveled by the block in terms of m, k and k x=0 L = ? 3 Px V=0