Question

Please answer all not understanding:

1. Volumetric expansion coefficients of simple materials are often well catalogued. However, the thermal expansion coefficient β of a human body is less well known. This could affect the human body\'s specific gravity and, therefore, measurements of its body/fat ratio. Suppose that a human body of weight w0 (on dry land) is placed on a scale while completely immersed in formaldehyde of temperature T1. Once the temperature increases by ΔT, the scale reading drops by Δw. Derive an expression for β in terms of ΔT, w0, and Δw by assuming that the ratio of the formaldehyde ρf and the initial density of the body ρb is R = ρf /ρb. Assume also that ρf does not change when heated.

If the body weighs 224.3 lb on dry land and his weight reading lowers by 0.237 lb when the formaldehyde is heated from 66.40oF to 88.60oF, calculate the coefficient of volume expansion of the body.* Assume R = 0.720.

* The coefficient β will likely vary widely from one human body to the next. The numerical value computed here should not be considered factual.

2. The superheroine Xanaxa, with a mass of 66.3 kg, is in a hair-raising chase after the 74.3-kg arch-villain Lexlax. She leaps from the ground to the top of a 195-m-high building, then dives off and comes to rest at the bottom of a 16.7-m-deep excavation, where she finds Lexlax and neutralizes him. Does all this bring about a net gain or a net loss of gravitational potential energy?

By how much? Answer with a positive number. Take g = 9.81 m/s2.

3. A boy shoves his stuffed toy zebra down a frictionless chute, starting at a height of 1.25 m above the bottom of the chute and with an initial speed of 1.33 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with coefficient of kinetic friction 0.245. How far from the bottom of the chute does the toy zebra come to rest? Take g = 9.81 m/s2.

4. A 7130-kg car is travelling at 24.8 m/s when the driver decides to exit the freeway by going up a ramp. After coasting 418 m along the exit ramp the car\'s speed is 12.4 m/s, and it is h = 12.5 m above the freeway. What is the magnitude of the average drag force exerted on the car?

5. An undamped 2.52-kg horizontal spring oscillator has a spring constant of 28.7 N/m. While oscillating, it is found to have a speed of 3.35 m/s as it passes through its equilibrium position. What is its amplitude of oscillation?

What is the oscillator\'s total mechanical energy as it passes through a position that is 0.568 of the amplitude away from the equilibrium position?

6.

Answer 1