Consider a conical pendulum with a bob of mass m = 79.0 kg on a string of length L = 10.0 m that makes an angle of = 6.00⁰ with the vertical. (Consider +î to be towards the center of the circular path and +j to be upward.) m (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. Ni+ Nj (b) Determine the radial acceleration of the bob. m/s²
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- Computation. Three objects are connected as in the figure with mд-7 kg, mB=6.43 kg, and mc-11.4 kg. The strings and frictionless pulleys have negligible masses, and the coefficients of friction between the block and the table are s-0.67 and u-0.151. If the system is released from rest, find the magnitude of its acceleration. [Hint: As part of your solution, check to see if block B experiences static or kinetic friction.] MA a = JACOPERTE mc E OL MB _m/s² Record your numerical answer below, assuming three significant figures. Ca O @ ✰ ✰ 0 A D 10:14 PM 10/19/2022 *** 2In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle = 25.6°. The slab has length L = 43.4 m, thickness T = 6.23 m, and width W = 13.6 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.351. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.42 cm² and will snap under a shearing stress of 3.57 × 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.Two blocks of mass m1 = 3.0kg and m2 = 2.5kg are attached with a rope. The rope goes around several ideal pulleys. Two of the pulleys are attached directly to the ceiling (grey shaded region at the top) and will not move up or down. The lower pulley will move with block 1. Block 1 is free hanging and will move vertically. Block 2 rests on an inclined ramp at angle θ = 30°. The ramp is frictionless. Block 1 is observed to accelerate upwards. The experiment is done on earth, g = 9.8 m/s2 What is the tension in the long rope? by using variables only
- a 1.34 kg ball is connected by means of two massless strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the (a) tension in the lower string, (b) magnitude of the net force on the ball, and (c) speed of the ball? (d) What is the direction of the net force?A person pushing a uniformly-loaded 31.7 kg wheelbarrow of length L with pushing force P is attempting to get it over a step. The maximum horizontal force that the person can apply is P, = 233 N. What is the maximum height h of the step, expressed as a fraction n of the wheel's radius R. that the person can get the wheelbarrow over? The gravitational acceleration is g = 9.81 m/s². 8459 R Incorrect hnRConsider a conical pendulum with a bob of mass m = 58.0 kg on a string of length L = 10.0 m that makes an angle of 8 = 2.00° with the vertical. (Consider +î to be towards the center of the circular path and +j to be upward.) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. NI+ Nj (b) Determine the radial acceleration of the bob. m/s²
- The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 5.00 m long, and the upper end of the cable is fastened to the arm at a point 3.00 m from the central shaft. (a) Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 30.0◦ with the vertical. (b) Does the angle depend on the weight of the passenger for a given rate of revolution?A mass m is suspended from a massless spring of natural length 90 cm with the spring constant k = 10 Nm and causes the spring to extend by 7.9 cm. Assuming the gravitational field strength g = 9.8 ms², calculate the value of the mass on the spring. Give your answer in Sl units. Answer: Choose... +In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle 8 = 22.8°. The slab has length L = 48.9 m, thickness T = 6.61 m, and width W = 12.7 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.312. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.47 cm² and will snap under a shearing stress of 3.59 x 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.
- Masses m₂, m₂, m3 and om are connected together as shown in the figure below. All the surfaces are smooth. If m₁ = 3.2kg, m₂ = 2.8kg, m3 = 3.8kg, om = 1.3kg and = 55°, calculate a) the acceleration of the system. b) the normal force between m3 and ōm. 7²1 7122 In+one 183A small box with a weight of 35.0 N is placed on top of a larger box that has a weight of 80.0 N. The system of two boxes is at rest on a horizontal surface (the larger box is in contact with the surface). You apply an additional downward force of 30.0 N to the top of the small box by resting your hand on it. For this problem, use g = 10 N/kg. (a) What is the magnitude of the force exerted on the large box by the small box? (b) What is the magnitude of the force exerted on the large box by the surface? Now, imagine that the horizontal surface is the floor of an elevator, and the boxes are in the elevator, which has an acceleration directed downward of 1.00 m/s?. (c) What is the magnitude of the force exerted on the large box by the small box in this case? (d) What is the magnitude of the force exerted on the large box by the surface in this case? NA rod of mass M and length L is attached to a wall with a pin joint, around which the rod is free to rotate. A horizontal rope attached to the end of the rod holds the rod at an angle θo to the horizontal. Express your answer in terms of M, L, θo, and g (and no other variables). What is the tension in the rope? Suddenly the rope breaks. As a result, the rod swings down. Immediately after the rope breaks, what is the rod’s angular acceleration?