A particle is constrained to move in a circle in the vertical plane x-y. Using D’ Alembert principle show that for equilibrium, xy ̈ − yx ̈ − gx = 0.
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A particle is constrained to move in a circle in the vertical plane x-y. Using D’ Alembert principle show
that for equilibrium,
xy ̈ − yx ̈ − gx = 0.
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- And don't worry about whether the passengers would actually survive the trip. They are lightweight crash test dummies. NTC A cart of mass m= 347 kg is going around a circular loop-the-loop. There is no motor. The cart moves only under the influence of gravity. Ignore friction and let g = 9.81 meters per second squared. The loop has a radius of r meters. When the cart is at the top of the loop, the normal force on the cart (exerted by the track) pushes down on the cart with a force of N = 1,330 newtons. When it is at the bottom of the loop, the cart has a speed of 30.7 meters per second. What is the radius of the loop (in units of meters)?Find x such that the system is in equilibriumConsider two boxes initially at rest as shown, each of mass 5.0 kg, that are connected by a massless string over a pulley of radius 5.0 cm and rotational inertia equal to 4.0 x 10-3 kg·m². The coefficient of kinetic friction between the inclined surface and the box is 0.15. Find the speed of the boxes just after they have moved 1.0 m. Justify approach taken as you begin your solution. 30° m m
- A 250 g piece of kryptonite is attached to a 90 cm long masless string to form a pendulum. At its highest point (Point A) the string makes an angle of 55 degrees with the vertical. Its lowest point is Point B and Point C is where the string makes an angle of 35 degrees with respect to the vertical. Find the tension in the string and angular acceleration of the rock at (a) Point A, (b) Point B and (c) Point C. (a) Draw a free body diagran of the kryptonite, including all relevant angles and axes at Point A, Point B, and Point C. (Three total FBD) (b) Find the angular speed, angular acceleration and tension in the string at Point A. (c) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point B. (d) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point C.A box descends a ramp and lands on a surface. The box exits the side of the table as it meets the bottom of the tamp, becoming a horizontal projectile. It lands x metres away from the table. The same ramp may be rolled down by a solid sphere with the same coefficient of friction, mass, and height. Will the sphere land a long way away? fewer than a lot more At a similar size B. Have a paragraph-length description of the logic.A block of mass mA=20kg on an inclined plane and a bucket of mass mbucket=16kg are attached to the ends of a massless string passing through a massless pulley as shown in the figure below. The inclined plane makes an angle of θ=46o with the horizontal and the coefficients of kinetic and static friction are μk=0.21 and μs=0.58. The system is initially at rest and a student starts to fill the bucket with balls, each of whose mass is 100 grams, one at a time until the system starts to move. Determine the number of balls the student placed in the bucket. Take g=9.80m/s2 and please note that the number balls must be an integer!