2. Mass m₁ slides without friction on a plane inclined at 40° above horizontal plane. It is attached to a second mass m₂ by a light string. If m₁ = 5kg, m₂ = 4kg, determine the acceleration of each block and the tension of the string.
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- 3. Two blocks with unequal masses, M and m (M> m), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible. a. If one of your classmates calculated that, once released, the acceleration of the blocks would be g, '6 without doing any calculations, say whether or not this could be a reasonable value for the acceleration. Draw and label a free body diagram (FBD) for each block. (Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.) Rank the relative magnitudes of all forces in your FBDS. (I'm looking for a single ranking that includes every different force drawn and labeled in both FBDS, separated by , or =.) heavy block: b. light block: relative sizes of all forces in FBDS: C. Use the FBDS from the previous part, and Newton's 2nd Law, to derive an expression (in terms of M, m and g) for the acceleration of the blocks once…1. Five Bodies are available in a region where g = 9.785 m/s2 have the following data: A.Body A weighs 10 kNB.Body B has a mass of 10 slugsC.Body C weighs 1,000,000 grainsD.Body D has a mass of 1.5 tonsE.Body E weighs 20 kg Required:Determine the following:A.The total mass in kg and in hylB.The total weight in kN and in poundalsIt is fixed at one end of the D pipe.Collar A can move on pipe D and collar B on pipe A without friction.The general equation for the position of the ring A is SA, the general equation for the velocity of the B ring is VB. The friction coefficient between the C ring and the B pipe is 0.3 .All rings weigh 98.1N .Neglect the weight of the pipes. SA=(20+0.4t2+0.01t4)i+0j VB=0i+(0.3t2+25)j If ?=25°,draw the free body diagram and kinetic diagram for B and C rings for t = 4 s and find the unknown force values. Also calculate the relative acceleration of Rings B and C and the vectorial value of the acceleration of the X-Y axis with respect to the origin.
- Example 4.13 Connected Objects Goal Use both the general method and the system approach to solve a connected two-body problem involving gravity and friction. Problem A block with mass m, = 3.90 kg and a ball with mass m, %D 7.70 kg are connected by a light string that passes over a frictionless pulley, as shown in Figure 4.23a. The coefficient of kinetic friction between the block and the surface is 0.300. (a) Find the acceleration of the two objects and the tension in the string. m2 (b) Check the answer for the acceleration by using the system approach. Figure 4.23a Two objects connected by a light string that passes over a frictionless pulley. y Strategy Connected objects are handled by applying Newton's second law separately to each object. The free-body diagrams for the block and the ball are shown in Figure 4.23b, with the +x-direction to the right and the +y-direction upwards. The magnitude of the acceleration for both objects has the same value, |a,| = |a,| = a. The block with…5. An egg of mass 50g is in the stiff box of mass 300g. surrounded on all sides by padding that constrains the egg in place. A force of F= (4.61N)I + (2.80N)j acts on the outside of the box, in addition to the force of gravity. a. Find the acceleration of the egg box system b. What is the net force of the egg?3. Two blocks with unequal masses, M and m (M> m), are connected by a light, very long string passing over a pulley of negligible mass, as shown in the figure, and then released. Friction is negligible. 4 a. If one of your classmates calculated that, once released, the acceleration of the blocks would beg, without doing any calculations, say whether or not this could be a reasonable value for the acceleration. b. Draw and label a free body diagram (FBD) for each block. (Be sure your drawings show clearly any information you know about the directions and relative magnitudes of the forces.) Rank the relative magnitudes of all forces in your FBDS. (I'm looking for a single ranking that includes every different force drawn and labeled in both FBDS, separated by , or =.) heavy block: light block:
- 2. A 2 kg box is suspended in the air. Attached to each corner of the box is a rope. All 4 ropes are the same length and are attached to 1 point in the ceiling. Draw the FBD of the box and find all the forces acting on it. 3 A 1 5 00-kg car starts from rest and takes 10s to reach a sneed ofTwo masses m1-10 Kg and m2-13 Kg are connected with string and pulled with a force F=22 N that makes an angle 0=53° with a smooth horizontal surface as shown in the figure. Find the tension in the string (Newton). m m2 A. 2.878 B. 8.141 C. None D. 11.5110. An object with weight W is dragged along a horizontal plane by a force acting along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle e with the plane, then the magnitude of the force is F = u sin 0 + cos 0 where u is the coefficient of friction a. Find the rate of change of F wrt 0. b. The value of 0 at maximum or minimum value of F.
- 2. A 10-kg body is suspended by means of a string. Another string is attached to the bottom of the body and a 5-kg body is suspended from the lower end of the lower string. Find the tension in each string. 3. Two strings support a small 8-kg body. Find the tension in the strings if they both make 30o with the vertical. 4. A weight of 100 newton is suspended by means of a string. It is then pulled aside by a horizontal force until the string makes an angle of 37o with the vertical. Find the tension in the string and the horizontal force for this equilibrium position. 5. The following three forces act on a particle: 30 N at 30o with the x-axis, 50 N at 135o with the x-axis, and 20 N along the negative x-axis. Find the fourth force on the particle which will keep it in equilibrium. 6. Two forces which are equal in magnitude act on a body. To keep the body in equilibrium, a third force which is equal in magnitude to each of the two forces is required. What is the angle between the two…1. A Christmas light hangs on a series of strings as shown in the figure below. The tension on string a, Ta, is 0.48 N. 42° J a d C K 25° 30° m (a) What is the tension on string b? (b) What is the tension on string c? (c) What is the tension on string d? (d) What is the mass of the Christmas light, m, in grams?2. Assume that the masses A and B are 4 kg and 10 kg, respectively. If the coefficient of friction is 0.30, find the acceleration if A В 30° a. the system is moving up the plane, b. the system is moving down the plane.