Determine tension in cables and accelerations of block

Reference no: EM13811013

1) A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end of a rope of length 1. Determine the angle θ for which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the bag.

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2) Beginning from rest when θ =15°, a 35-kg child slides with negligible friction down the sliding board which is in the shape of a 2.5-m circular arc. Determine the tangential acceleration and speed of the child, and the normal force exerted on her (a) when 0=30° (b) 8=90°

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3) Determine the tension in the cables and accelerations of block A and B. Take g = 10 m/s²

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4) A small object A is held against the vertical side of the rotating cylindrical container of radius r. If the coefficient of static friction between the object and the container is μ_s, determine the minimum angular velocity ω of the container which will keep the object from slipping down the vertical side.

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5) The member OA rotates about the horizontal axis through 0 with a constant counterclockwise angular velocity to ω = 3 rad/sec As it passes the position θ = 0, a small block of mass 0.1 kg is placed on it at a radial distance r = 18 inches. If the block is observed to slip at θ = 50°, determine the coefficient of static friction ps between the block and the member.

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6) Calculate the acceleration of the 100-lb cylinder for each of the two cases illustrated. Neglect friction and mass of pulleys. Note lb here is unit of force. (Take g = 32.2 ft/s²)

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7) Find the minimum value of T (i.e. Tmin) for which the block shown in the figure will start to slip. Next, assume T = 2Tmin and compute the acceleration of the block.

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8) A stretch of highway includes a succession of evenly spaced dips and humps, the contour of which is approximately given by y = bsin(2Πx/L) quite probable in San Francisco]. What is the maximum speed at which the car A can go over a hump and still maintain contact with the mad? If the car maintains this critical speed, what is the normal force that it experiences from the ground at the bottom of a dip? The mass of the car is m.

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9) The small cart is nudged with negligible initial speed from its horizontal position at A onto the parabolic path, which lies in a vertical plane. Neglect friction.

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a) Find the expression of the normal force N as a function x

b) Show that N is always > 0 for all values of k.

10) For the pulley system shown, find the acceleration of the load m and the tension in the cables. Assume frictionless surfaces, massless pulleys and inextensible cables. The pulleys C and D are at the same level.

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Reference no: EM13811013

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