CP Riding a Loop-the- Loop. A car in an amusement park ride rolls without friction around a track (Fig. P7.42). The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B?)? (b) If h = 3.50R and R = 14.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C. which is at the end of a horizontal diameter. Show these acceleration components in a diagram, approximately to scale.
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- You push a .50kg block against a spring (k=3100 N/m),compressing it by .12m. The block is then released from rest and the spring pushes the block away. The spring and the block lose contact and the block collides with a second block of twice the mass. The two blocks slide together down a frictionless track consisting of a flat straightaway and a vertical, semi-circle of radius 40cm. What is the speed of the blocks when they have travelled halfway up the semicircle part of the track? What is the magnitude of the normal force on the two blocks at that same location?arrow_forwardA car in an amusement park ride rolls without friction around the track shown. It starts from rest at point A (it's location in the picture) at a height h above the bottom of the loop. Treat the car as a particle. a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B, which B being the top of the loop)? b) If h = 3.50 R and R = 20.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C (labeled), which is at the end of a horizontal diameter of the loop. Show these acceleration components in a diagram, approximately to scale.arrow_forwardA smooth block is set at the top of a smooth track. There is no friction between the block and track. We would like the block to make its way through the entire track, and so it must stay on the track as it goes through the circular loop section. The block starts at rest, and the Radius of curvature for the loop is 10 meters. Use g = 9.8 m/s?. What is the minimum starting height H for the block if it is to make it through the loop while still staying on the track? Hint: At the top of the loop the Normal force will be zero in this situation. This is because we want a starting height that will give us just enough speed at the top of the loop to follow the circular path, no more, no less. H=? Rarrow_forward
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- A 148 g ball is released from rest H = 1.51 m above the bottom track. It rolls down a straight 45° segment, then back up a parabolic segment whose shape is given by y = x2/4, where x and y are in m. How high will the ball go on the right before reversing direction and rolling back down?arrow_forwardA 15.0 kg stone glides down (we neglect any type of rotation) on a snowy hill, starting from point A with a speed of 10.0 m/s. There is no friction on the hill between points A and B, but there is friction on the flat ground below, between B and the wall. After entering the horizontal rough region, the stone travels 100 m and collides with a very long and light spring, whose force constant is 2.00 N / m. The coefficients of kinetic and static friction between the stone and the horizontal ground are 0.20 and 0.80, respectively. How far will the stone compress the spring? A 20 m В VK15 m- Rough zone a) 22,2 m b) 16,4 m c) 45,78 m d) 100 m D. Concentraarrow_forwardIn the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h; = 4.5 cm and hy - 1.70 cm. With what speed must the ball be shot at point P for it to land at d= 4.0 cm? Ball Vo"arrow_forward
- Back when I was a kid, I loved to play with my Hot Wheels. Hot Wheels are miniature metal cars that race down lengths of flexible track. The track comes in segments that can be connected together. One thing you can do is make the cars Loop the Loop, as shown in the figure above. Starting at a height, h, the cars race down the track, traverse a circular loop of radius, R, without falling down at the top of the loop, and then continue racing along a section of level track. If the loop is 9 inches in diameter, what is the minimum height, h, from which the cars can start and still loop the loop without falling down at the top? Neglect friction and air resistance.arrow_forwardIn the figure, a solid 0.4 kg ball rolls smoothly from rest (starting at height H = 6.1 m) until it leaves the horizontal section at the end of the track, at height h = 1.9 m. How far horizontally from point A does the ball hit the floor? Number i H ! A Units 3arrow_forwardThe figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8° and released with initial velocity V 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if %3D the mass is increased? 3.arrow_forward
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