3. According to Hooke's law, the force F required to stretch a spring x units beyond its natural length is directly proportional to x. a. Write an equation which expresses the relationship between F and x. b. Suppose that it takes a force of 8 pounds to stretch a spring 8 centimeters long to a new length of 10.5 centimeters. Find the value of the constant of proportionality k, which is known as the spring constant. c. How much weight is needed to stretch the spring described in (b) to a length of 10.8 centimeters?

Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?

Find the intensities of earthquakes whose magnitudes are aR=6.0andbR=7.9.

Find the intensity of light at a depth of 12 meter if I0=14 and k=0.7. Round to two decimals.

Frictional Force The frictional force F between the tires and the road required to keep a car on a curved section of a highway is directly proportional to the square of the speed s of the car. If the speed of the car is doubled, the force will change by what factor?

A spring is stretched a distance x from its original length. The potential energy stored in the spring is directly proportional to x squared. The potential energy stored in the spring when it is stretched 0.25m is 600 J. Derive an equation for the potential energy stored in the spring. Note:  You must determine the value of the constant.

The following loads (in ounces) are suspended from a spring and the stated lengths (in inches) are obtained. Determine the spring constants and the equation that describes each spring. Predict the length of each spring when a weight of 15 ounces is suspended. (a) Force F 2 4 8 Length L 5.9 8.0 10.5 12.2 L(F) L(15) (b) Force F 8 Length L 7.4 10.3 13.7 16.9 L(F) L(15)

10) The Hurricane Hunters took the following measurements from a hurricane over They found that the air pressure and wind speed are related in the following way: y=-1.11x+1140 where x is the air pressure in millibars (kPa) and y is the maximum sustained wind speed in knots (nautical miles per hour). several days as it developed: Air Pressure (kPa) Wind Speed (knots) 924 129 933 110 946 67.3 140 958 86 120 991 41.3 100 1,002 35.7 車 920 910 Air Pressure (kPa) a) What does the y-intercept of this function represent? b) Using the model, what would be the wind speed of a hurricane with an air pressure of 969 kPa? Round your answer to the nearest knot. Wind Speed (knots)

The acceleration in cm/s? of a moving object is given by a distance travelled ( in cm) in the first 5 seconds, if when t = 0, v = 2 and s = 0 30 - 12t. Find the cm