Assume that you have been asked to look into purchasing some storage tanks for your company, and for the purchase of these tanks, you are given a budget of $1680. After some research, you find two tank manufacturers that meet your requirements. From Manufacturer A, you can purchase 16-m3-capacity tanks that cost $120 each. Moreover, the type of tank requires a floor space of 7.5 m2. Manufacturer B makes 24-m3-capacity tanks that cost $240 each and that require a floor space of 10 m2. The tanks will be placed in a section of a lab that has 90 m2 of floor space available for storage. You are looking for the greatest storage capacity within the budgetary and floor-space limitations. How many of each tank must you purchase?

1. Hydraulic jacks are one of the many tools humans use to develop a so-called "mechanical advantage". The basic idea is that a relatively small force applied to the smaller-area piston can counteract a relatively large force applied to the larger-area piston. F₂ a) Ignoring the weight of the fluid (i.e., ignoring changes in hydrostatic pressure due to the density of the fluid) and any friction between the piston and the sidewalls, show that F2 = F₁ AR A₁ in static equilibrium. b) The mechanical advantage of the hydraulic jack can be defined as the ratio of the force applied to piston 2 to the force applied to piston 1 in order to keep the system in static equilibrium. For circular pistons, use the relationship in part a) to plot the mechanical advantage as a function of the diameter ratio of the pistons. Explain the significance of this mechanical advantage. c) Consider a hydraulic jack in static equilibrium with both pistons at the same elevation. If you do not consider the weight of…

4. Pick three different whole numbers of ounces of beverage for Alice to drink and find her height after consuming each amount. Assume in each case that she starts out 5 feet tall.

A runner wants to run 10.0 km. She knows that her running pace is 7.5 miles per hour. How many minutes must she run?

An electric hot water heater consumes 3.1 kilowatts of electricity and converts it to heat. How long will it take the water heater to heat a 67 gallon tank of water from 10 degrees Celsius to 50 degrees Celsius? (1 kilogram of water is 0.37 gallons, 1 Calorie = 4200 J).  It may be helpful to refer back to the weekly handout for guidance on this problem. Your final answer should be in minutes (rounded to the nearest 10 minutes).

Pushing a Block and a Wedge 0 points possible (ungraded) In the following problem, you are asked to: i) Define the system and the environment: Identify which objects - the environment - interact with the object of interest - the system. Justify your choice of system: would a different choice also work? If not, why not? If so, why is the choice you made better? ii) Describe the interactions and the resulting forces: Identify the forces exerted on the object of interest by the other objects. iii) Draw the free body diagram of the object: Make sure that each force arrow is labeled with two subscripts - who is exerting the force and on whom is the force being exerted. The length of the arrows should represent qualitatively the magnitude of the force. a) c) M m 0 a F M m 0 A block of mass m rests on a frictionless wedge which has a mass M and whose surface makes an angle to the horizontal as Calculator