What is its length?
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A pendulum is
meters long. The time,
, in seconds that it takes to swing back and forth once is given by
. Suppose the pendulum takes
seconds to swing back and forth once. What is its length?
Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.
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- The sides of a small rectangular box are measured to be (1.90 ± 0.01) cm, (2.00 ± 0.02) cm, and (3.1 ± 0.1) cm long. Calculate its volume and uncertainty in cm³. a. Its volume is b. The uncertainty on its volume is cm³. cm³.Acre-feet (af) is a unit that some non-scientists unwisely use to measure volume of liquids. By definition 1 acre foot is one foot multiplied by 1 acre. 1 acre is equal to about 4 × 104 ft2 . 1. How many cubic feet are in an acre-foot?need help with questions 1 through 11
- 2.Newton's law of universal gravitation can be expressed by the equation F = G Mm r2 , where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G?Soccer fields vary in size. A large soccer field is 144 meters long and 84.4 meters wide. Hint a. What are its dimensions in feet? o Its length is ft. o Its width is b. What are its dimensions in inches? o Its length is o Its width is ft. in. in.
- Suppose a machine is invented to measure the amount of knowledge in a student’s head in units called “factoids.” One student is measured at F(t) = t³ − 6t² + 9t factoids at time t, where t is measured in weeks. a. Find the rate at which the student is gaining (or losing) knowledge as a function of time (be sure to give the units). b. During what time between t = 0 and 11 is the student losing knowledge? c. Sketch a graph of the function F(t).A rectangle has a length of (2.8 ± 0.2) m and a width of (1.7 ± 0.2) m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value. (a) Calculate the area and give its uncertainty. (Enter your answers in m2.) m2 ± m2 (b) Calculate the perimeter of the rectangle and give its uncertainty. (Enter your answers in m.) m ± mAn Olympic-size swimming pool is 50 m long, 25 m wide, and 2 m deep. In terms of volume, this pool, when full, holds how many kilogallons of water? Use the following equivalences: 1 gallon = 3.8 L 1 kilogallon = 103 gallon 1 L = 103 mL for water: 1 mL = 1 cm3 1 m = 100 cm [Numerical Problem: Just write the numerical answer without units. Express your answer to 2 significant figures in standard notation]
- Estimate the number of steps you would have to take to walk a distance equal to the circumference of the Earth. (We estimate that the length of a step for an average person is about 18 inches, or roughly 0.5 m. The radius of the Earth is 6.38 x 106 m.) 105 steps 108 steps 1011 steps 1015 steps O 1020 stepsThe extraterrestrials in an exoplanet in a distant galaxy have the following units to measure distances.1 dray = 12 elim; 1 toof = 24 dray; 1 chin = 1250 toof. a. Convert 2.4 chin to elim. __________________ elim b. The alien grows vegetables in 16.0 square dray (i.e., dray2) patch. Calculate the area of the patch insquare elim (i.e., elim2).____________ clim2Run up a flight of stairs as fast as you can, measure the time it takes and the height of one stair, and count the number of stairs. If you don't know your weight, measure that too. These measurements need not have three significant digits, but the calculated values do. Recall that 1 inch is about 2.54 centimeters, and 2.2 pounds is the weight of about 1 kg of mass.weight = 148.5 poundstime = 1.66 sheight of one stair = 18.5 cm, number of stairs = 12a. What is your power while running up stairs? Include units in your answer. b. The human body has an efficiency of about 28 percent. If you could maintain this stair-climbing pace around the clock, you could consume how many calories of food energy each day and not gain weight? (1 food calorie = 4186 joules)