Ex5: A force (F) is proportional to (x²) and has the value of (133N) when (x=2), Determine the work done by it moves in object from (x1) to (x-4) wlhere (x) in meter.
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- Given: The energy equivalent of one gallo of gasoline is 1.3 x 10 J. A compact car has a mass of 907 kg, and its efficiency is rated at 16.7%. (That is, 16.7% of the input energy available is delivered to the wheels.) Find the amount of gasoline used to accel- erate the car from rest to 25.1 Answer in units of gal. m/s.A swimming pool is round, full of contaminated water, and has an 11 foot radius. It is 11 feet tall and has 4 feet of water in it.How much work is required to remove all of the contaminated water by pumping it over the side? (Use the physical definition of work, and the fact that the weight of the contaminated water isσ=63.2lbs/ft3 )What is the dot product A•B if A = 2x - 3y and B = 15x + 10y?
- The dot product (3i - j)•B is?A vertical right-circular cylindrical tank measures 28 ft high and 14 ft in diameter. It is full of liquid weighing 62.4 lb/ft³. How much work does it take to pump the liquid to the level of the top of the tank? Set up the integral that gives the work required, in ft-lb, with y = 0 corresponding to the bottom of the tank. (Type an exact answer, using as needed.)Force = 4x ^ 4 - 3x. Find the work in mks units done by the force for a distance of x = 1 to x = 7:
- Problem 2: A certain spring has a spring constant k₁ = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant then changes to k₂ = 250 N/m as the spring is stretched to x2= 65 cm. From x₂= 65 cm to x3 = 89 cm the spring force is constant at F3 = 105 N.(a) What is the efficiency of an out-of-condition professor who does 2.00 × 105 J of useful work while metabolizing 510 kcal of food energy? (Enter your answer as a percentage. Enter a number.) % (b) How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 20%? (Enter a number.) kcal(a) What is the efficiency of an out-of-condition professor who does 2.30 × 105 J of useful work while metabolizing 490 kcal of food energy? (Enter your answer as a percentage. Enter a number.) % (b) How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 25%? (Enter a number.) kcal