Two objects with masses of 2.55 kg and 4.15 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine. (a) Determine the tension in the string. (b) Determine the acceleration of each object. (c) Determine the distance each object will move in the first second of motion if they start from rest.

5. A 2-kg sphere is attached to a massless rigid rod attached to a fixed pivot point O. The rigid rod and mass rotate in the horizontal plane. A moment is applied to the rod of magnitude M = 0.5t² N. m, where t is in seconds. The length of the rod is 0.5 m. Determine the speed of the sphere after the moment is applied for 5 seconds. M(t)

(e) Two blocks X and Y are connected by a light and inextensible string as shown in the figure below. The string passes over a light and smooth pulley. Block Y has a larger mass than block X. Assuming that the friction between block Y and the inclined plane is negligible, describe and explain the motion of the two blocks when the blocks are released. 30 deg

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2. Three blocks on a frictionless horizontal surfsce are in contact with eachother as shown below. A force F is applied to block 1 as shown. (a) Draw a free body diagram for each block. (b) Determine the acceleration of the system in terms of m1, m2, m3 and F. (c) Determine the net force on each block. (d) Determine the contact force each block exerts on its neighbors. (e) If |F| = 96N and m1 = m2 = m3 = 12kg, give numerical answers to the questions above. Do your answers make sense intuitively? mi mz M3

A 35-kg child rides on a 10-kg bicycle with 500-mmdiameter wheels. Determine the horizontal force necessary to push the child and bicycle On a level sidewalk.Neglect all friction except rolling resistance.

Ex.4 The coefficients of static and kinetic friction between the 100-kg block and the inclined plane are 0.30 and 0.20, respectively. Determine (a) the friction force F acting on the block when P is applied with a magnitude of 200 N to the block at rest, (b) the force P required to initiate motion up the incline from rest, and (c) the friction force F acting on the block if P = 600 N. 100 kg 200 H, = 0.30 HA = 0.20 15° LEC.4 FRICTION

To understand how the conservation of energy and Newton's second law can be combined to solve kinetic problems. As shown, a large globe has a radius R and a frictionless surface. A small block with mass m starts sliding from rest at the top of the globe and slides along the globe’s surface. The block leaves the globe’s surface when it reaches a height hl above the ground. The system’s geometry is shown for an arbitrary height h. (Figure 1) Note that the subscripts used in this problem is the letter l and not the number 1.   Consider what happens when the block leaves the globe’s surface. Which of the following statement or statements are correct? The net acceleration of the block is directed straight down. The component of the force of gravity toward the globe’s center is equal to the normal force’s magnitude. The force of gravity is the only force acting on the block.Consider what happens when the block leaves the globe’s surface. Which of the following statement or statements are…

A slender bar with a length of 2 ft is pin-connected with a roller positioned on a smooth horizontal surface. The bar is at rest initially, and a horizontal force F is applied to the roller. If F = 13 lb and the weight of the bar is 10 lb, calculate the magnitude of the acceleration of the roller at that instant by neglecting the mass and the size d of the roller. Present your answer in ft/sec² using 3 significant figures. 2 ft F

(c). A 4 kg collar C slides on a horizontal rod between 2 springs A and B shown in FigureQ2(c). Initially the system is at rest and assume no friction between the collar and therod.(i) If the collar is pushed to the right until spring B is compressed 50 mm and released,using work and energy principle, determine the distance travel by the collar.