What? This problem again? Not exactly. A block with mass m,ị = 3.00 kg sits on a horizontal table and is attached to a rope. The rope then passes over a MASSIVE pulley this time and is attached to a block of mass m2 = 2.00 kg, which hangs vertically (see picture). The coefficient of kinetic friction of the interface between the table and m, is 0.1. You may assume the pulley section is a disk with a mass of 2 kg. We will keep the pulley frictionless for brevity. Ideal disk pulley with mass Find the acceleration of the blocks using your choice of either Newton's Laws or the energy conservation method. Yes, I can actually read your minds from here; of 2 kg and the answer is no, you do not need the radius of the pulley.
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- The wheels, axle, and handles of a wheelbarrow weigh W = 57 N. The load chamber and its contents weigh W₁ = 563 N. The drawing shows these two forces in two different wheelbarrow designs. To support the wheelbarrow in equilibrium, the man's hands apply a force to the handles that is directed vertically upward. Consider a rotational axis at the point where the tire contacts the ground, directed perpendicular to the plane of the paper. Find the magnitude of the man's force for both designs. F F (a) F = (b) F = i i W 0.400 m ¹0.700 m 0.200 m (a) > > 0.600 m' 0.700 (b)A block of mass m, = 2.45 kg and a block of mass m, = 5.65 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of e = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Use g=9.8 m/s2. М, R m2 (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley NThe figure shows a simple model of a seesaw. These consist of a plank/rod of mass mr and length 2x allowed to pivot freely about its center (or central axis), as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward. The magnitude of the acceleration due to gravity is equal to g. Suppose that the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answered the first part correctly.)What is the angular acceleration α of the rod immediately after it is released? Take the counterclockwise direction to be positive. Express α in terms of some or all of the variables mr, m1, m2, x, I, and g.
- 9. A mass m1 = 9.50 kg is connected by a light string that passes over a pulley of mass M = 10.5 kg sliding on a horizontal surface (see figure). The coefficient of kinetic friction between the mass m2 and the surface is 0.25. There is no slippage between the string and the pulley. What is the magnitude of the tension that is acting on mass m,? (The moment of inertia of the pulley is V½Mr2.) N 60 ssf60 ssfo 11.5 kg to a mass m2 ssf60 ssf60 ssfo 60 ssf60 ssf60 ssf60f60 sf6ssf60 ssf60 ss sf60 ss60 ssf60 m1 160f6 ssloU ssf60 ssf60 ssf60 ssf60 ssf60 f60 ssf60 ssf60 ssf6 O ssf60sf60 ssf60 ssf60 ssfoThe figure below shows a human arm that weighs 44.4 N. The arm is extended outward and is motionless. The gravitational force F on the arm acts at point A, a distance of 0.290 m from the shoulder joint, which is represented by point O. The shoulder pushes down and to the right on the humerus bone of the arm with a force F at point O, at an angle 8 as shown. The deltoid muscle pulls back on the arm toward the shoulder with a tension force F,. This tension force acts at a point 0.080 m to the right of point O, and it is directed up and to the left, at a 12.0° angle with respect to the horizontal. 0.080 m -0.290 m Find the magnitudes (in N) of the forces F, and F. (Enter your answers to the nearest whole number. Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) N NA 16.0-kg child swings in a swing supported by a chain, 5.06 m long. The tension in thechain at the lowest point is 200 N.a. Find the child’s speed at the lowest point.b. Find the force exerted by the seat on the child when the chain makes a 30◦ anglewith the vertical. (Ignore the mass of the seat, and the small angular acceleration atthis point.)Answer Box:a = 3.69 m/sb = <0.5, 157.8> N
- Consider the system shown in the figure below with m1 = 30.0 kg, m2 = 13.4 kg, R = 0.300 m, and the mass of the pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.50 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. a) Calculate the time interval required for m1 to hit the floor (in second). b) Calculate the time required again if the pulley were massless (in second)?Two buckets of mass ?1=21.1 kg and ?2=11.9 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.13 kg and a radius of ?p=0.350 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction. The buckets are released from rest and begin to move. If the larger bucket is a distance ?0=1.85 m above the ground when it is released, with what speed ? will it hit the ground?As a torque activity, your Physics TA sets up the arrangement shown below. m2 A uniform rod of mass m, = 153 g and length L = 100.0 cm is attached to the wall with a pin as shown. Cords are attached to the rod at the r, = 10.0 cm and r, = 90.0 cm mark, passed over pulleys, and masses of m, = 226 g and m2 = 127 g are attached. Your TA asks you to determine the following. (a) The position r3 on the rod where you would suspend a mass m3 = 200 g in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, what force (magnitude and direction) does the pin exert on the rod? Use standard angle notation to determine the direction of the force the pin exerts on the rod. Express the direction of the force the pin exerts on the rod as the angle 0F, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). r3 m Fp %3D OF (b) Let's now remove the mass m3 and determine the new mass ma you would…
- A uniform thin rod of mass m = 3.2 kg and length L = 1.5 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 6.5 N, F2 = 2.5 N, F3 = 15 N and F4 = 15 N. F2 acts a distance d = 0.14 m from the center of mass. a. Calculate the magnitude τ1 of the torque due to force F1, in newton meters. b. Calculate the magnitude τ2 of the torque due to force F2 in newton meters. c. Calculate the magnitude τ3 of the torque due to force F3 in newton meters. d. Calculate the magnitude τ4 of the torque due to force F4 in newton meters. e. Calculate the angular acceleration α of the thin rod about its center of mass in radians per square second. Let the counter-clockwise direction be positive.Two boxes are connected to a cord, and the cord is hung over a pulley connected to the ceiling, as shown in the figure below. m1 The masses of the boxes are m₁ = 16.0 kg and m₂ 10.0 kg, the mass of the pulley is M = 5.00 kg, and the radius of the pulley is R = 0.300 m. Box m₂ is initially on the floor, and box m₁ is initially 5.00 m above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the cord is small enough to be ignored, 1 and the cord does not slip on the pulley, nor does it stretch. = At ₂ MOR (a) How much time (in s) does it take box m₁ to hit the floor after being released? At ₁ = mq S (b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m₁ to hit the floor if the mass of the pulley were neglected.) = SChad gets on a roller coaster. Chad and the cart rolls down the frictionless loop with a constant speed of 7.4 m/s. The mass of Chad and the cart is 0.75 kg and the radius of the loop is 0.86 m. Since the cart has a smaller dimension than the loop, the cart can be viewed as a point particle. What is the normal force at the top and bottom points? The magnitude of the gravitational acceleration is 9.8 m/s^2. Draw a free body diagram.