1. The bucket of the excavator at a construction site is subjected to 1200-lb and 700lb digging forces at its tip. Determine the magnitude and direction of the resultant force acting on the bucket. Use ‘given, find, equation, solution’ format to solve, and show all work.

2. During the power stroke of an internal combustion engine, the 400lb pressure force pushes the piston down its cylinder as shown. Determine the components of that force in the direction along and perpendicular to the connecting rod AB. Use ‘given, find, equation, solution’ format to solve, and show all work.

3. The force due to buoyancy allows a balloon to rise through the air
The force due to buoyancy allows a balloon to rise through the air. If Fb = V, where  = specific weight of air and has a value of 9.8 kN/m3, and V is the volume of the air inside the balloon, estimate the volume of a balloon required to lift everyone in this room. Use ‘given, find, equation, solution’ format to solve, and show all work. CLEARLY list all your assumptions and include all units.