Batman, whose mass is 122 kg, is holding on to the free end of a 15.9 m rope, the other
end of which is fixed to a tree limb above.
He is able to get the rope in motion as only
Batman knows how, eventually getting it to
swing enough that he can reach a ledge when
the rope makes a 50.4
◦
angle with the vertical.
The acceleration of gravity is 9.8 m/s
2
.
How much work was done against the force
of gravity in this maneuver?
Answer in units of J.

Heat is added to a piston-cylinder device filled with 2 kg of air to raise its temperature 400 c from an initial temperature of t1 27 cand pressure of pi 1 mpa. the process is isobaric process. find a)-the final pressure p2 b)-the heat transfer to the air.

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.