Because the centripetal force is provided by spring for this apparatus, the centripetal force at a given distance r is fixed by the spring constant of the spring. therefore, mv^2 should be constant for a given radius r. calculate the quantity mv^2 for the four data points taken at the same radius r. describe the agreement of those values.
there were only 3 data points: 0.43825, 0.48825, and 0.53825 and the mv^2 were calculated for each which i have written below the question in the picture for each of the three data points (1.30, 1.27, and 1.40). what is the agreement of these values?

An air bubble of volume 20 cm³ is at the bottom of a lake 40 m deep, where the temperature is 4.0°c. the bubble rises to the surface, which is at a temperature of 20°c.take the temperature of the bubble’s air to be the same as that of the surrounding water. just as the bubble reaches the surface, what is its volume?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

Work out sian speed for the first 30 minutes of her journey. give your answer in km/h.