Q5. Two particles, A and B, are connected by a light inextensible string which passes through a hole in a smooth horizontal table. The edges of the hole are also smooth. Particle A, of mass 1.4 kg, moves on the table, with constant speed in a circle of radius 0.3 m around the hole. Particle B, of mass 2.1 kg, hangs in equilibrium under the table, as shown in the diagram. (a) Find the angular speed of particle A. (4) (b) Find the speed of particle A. (2) (c) Find the time taken for particle A to complete one full circle around the hole. ←0.3m->> B
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- A string is wrapped around a heavy wheel of radius R = 0.5 m. A block of mass m = 10 kg hangsfrom the other end of the string. When let go, the block falls with an acceleration of a = 5.8 m/s2.The wheel rotates about its center with angular acceleration α, but otherwise does not move.The string does not slip.a) Draw a free body diagram and write Newton’s 2nd law for the block Do not substitute any numbers.b) Draw a free body diagram and write Newton’s 2nd law for the wheel. Do not substitute any numbers.c) What is the tension in the string, T? Write your answer to two decimal placesd) What is the angular acceleration, α? Write your answer to two decimal places.e) What is the moment of inertia of the heavy wheel? Write your answer to two decimal placesIn one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is an inertial force sensed and used by the riders to explain events in the rotating frame of reference of the barrel. Explain in an inertial frame of reference (Earth is nearly one) what pins the riders to the wall, and identify all forces acting on them.A 4.30-kg object is attached to a vertical rod by two strings as shown in the figure below. The object rotates in a horizontal circle at constant speed 6.75 m/s. 2.00 m (3.00 m 2.00 m (a) Find the tension in the upper string. N (b) Find the tension in the lower string. N
- At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 5 m/s, and a 50-kg person feels a 125-N force pressing against his back. What is the radius of a chamber in km?A toy airplane is moving in a circle at constant speed (uniform circular motion) at the end of a guide wire. Which one of the following is TRUE regarding the direction of the Tension force of the guide wire? O It changes from time to time as the toy plane moves; sometimes perpendicular and other times parallel to the velocity of the plane. O Il is parallel to the velocity of the toy plane at all times. O There is no Tension force since the toy plane moves at constant speed. O It is perpendicular to the velocity of the toy plane at all times 424 V. M Opion Comman Controrm₂ A mass of 33.0 g on the frictionless table in the diagram is connected by a string through a hole in the table to a hanging mass of 27.0 g. With what speed (in m/s) must the table mass rotate in a circle of radius 1.19 m if the hanging mass is to remain hanging at rest, assuming that the local acceleration due to gravity is 9.80 m/s²?
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- A child ties a 0.3 kg stone to one end of a string. Holding the other end, the child whirls the stone in a vertical circle of radius 0.9 m. a. At the top of the circle, the speed of the stone is 8 m/s. What is the tension in the string? Draw the free body diagram. b. At the bottom of the circle, the speed of the stone is 9 m/s. What is the tension in the string? Draw the free body diagram. c. The string can withstand a maximum tension of 40 N before it breaks. The child whirls the stone faster and faster. At what point on the circle does the string break? Show this point on a circle, then draw the trajectory of the stone after breaking. Make sure you clearly show the direction of the stone immediately after the string breaks. d. What is the speed of the stone as the string breaks?A 560 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts a 8.0 N vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the launch point. At what horizontal distance left of the loop should you launch?A heavy chandelier with mass 180 kg is hung by chains in equilibrium from the ceiling of a concert hall as shown in the figure below, with 0, = 30.0° and 0, = 56.0°. Assuming the chains are massless, what are the tensions F,, ER, and F in the three chains? F72 FT1 FT2 FT3 = z z z