Four balls, each of mass m, are connected by four identical relaxed springs with spring constant k. The balls are simultaneously given equal initial speeds vdirected away from the center of symmetry of the system as shown in (Figure 1) .

a- As the balls reach their maximum displacement, their kinetic energy reaches zero why?

b- Each of the balls will move outwards to a maximum displacement d, from its initial position. Use geometry to find x, the distance each of the springs has stretched from its equilibrium position. (It may help to draw the initial and the final states of the system.)

Express your answer in terms of d.

c-

Find the maximum displacement d of any one of the balls from its initial position.

Express d in terms of some or all of the given quantities k, v, and m.

with steps

You have been consulted by the mobile phone company hookup about a new augmented reality product called “brows”. they want to develop an alternative to google glasses, which, you recall, is a proposed new product which plans to superimpose a whole range of wireless google services over the user’s ordinary vision of the world. these appear in little circles and ovals, and let you phone people, take photographs, navigate across cities and inside buildings, find shops and update your social media. brows would do this too, but not be limited to special google services. the user would wear a small cylinder-shaped device designed to fit on top of their existing eyewear (glasses or sunglasses). it would project a reversed image onto the inside of the lenses, the reflection of which would be in focus for the user. instead of voice control, the user would control the device by eye and neck movements, which the device would track. the device would connect via bluetooth to the user’s phone, which would supply most of the computing power and wireless connectivity. hookup also wants to know what existing services would be most in demand, and which would not work well with brows. using your knowledge of augmented reality, wearable technology and interface design, is the project feasible? if not, why not? if feasible, how could the product need to be modified for a better experience?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

An object moves from position +34m to the position -15m in 15 seconds. what is the total displacement? what is the total velocity?