In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps. An engineer has done a survey and found that almost no one complains if the force is no more than 50 N. With a slope equal to 5°, what force must a person exert, assuming a 30 kg grocery cart (full of groceries)? Assume friction (wheels against the ground, wheel on the axle, and so on), can be accounted for by a coefficient equal to 0.10.

Problem 4: Buoyancy I Pontoon bridges use buoyant forces to support loads. This problem will ask you to consider a 10 ft section of the pontoon bridge sketched below. The bridge deck is 4 ft wide, and each 10 ft section has five 55 gallon drums on each side. Each drum has a diameter of 22 in, so the cross-sectional area of each drum is 2.64 ft², and each drum is 2.79 ft tall. Assume the bridge deck and the bracing system for the drums weigh 2300 lb per 10 ft section but occupy negligible volume. The bridge floats in water with y = 62.3 lb/ft³. Part A What is the cross-sectional area of all ten drums? [ft²] Part B What is the volume of all ten drums? [ft³] Part C When the bridge is unloaded, what length of the drums will be underwater? [ft] PLAN VIEW ∞∞∞∞0 ooooo SECTION VIEW Part D How much weight can each 10 ft section carry without sinking? [lb]

A beam with length L is fixed at both ends. It is loaded with a concentrated force P at L/3 from the first support. Draw the loading diagram. If the beam has a length of 10 m, cross section of 200x200mm, and force P is 10 kN, what is the deflection at midspan (in mm)?