Which of the following statements are true? a. When you jump into the air, the floor does work on you, increasing your mechanical energy. b. Work done by frictional forces must always decrease the total mechanical energy of a system c. Compressing a given spring 2.0 cm from its unstressed length takes more work than stretching it 2.0 cm from its unstressed length d. None of these statements are true. e. The total energy of a system cannot change.

Answer & Explanation :

a) No work done by frictional force accelerates a system like(spurter, spinter, runner etc ) which increases the total mechanical energy of the system. The given statement is false.

c) External force acting on the system, can do mechanical work , which changes the total energy of the system.The given statement is false.

d)Work done on the spring (W=1/2k(dx)2), from the equation work done proportional to square of compression or elongation. From the given data both elongationa and compression is same, work done is same.The given statement is false.

e)When you jump into air , work must be done againest gravity. Increase in mechanical energy of the jumper is its internal energy and not from the floor.The given statement is false.

Therefore,None of these statements are true.(b is correct)

The answer is: d. None of these statements are true.

Explanation:

a) When jumping in the air, the work is done due to gravity, therefore, the increase in mechanical energy is equal to the internal energy, therefore it is false.

b) No work done by friction force accelerates a system due to an increase in total mechanical energy, therefore it is false.

c) The work done by the spring from a work done proportionally equal to the square of the compression. According to the data provided, the elongation and compression are exactly the same and therefore the work done is the same, therefore it is false.

e) The external force acting on a system can perform mechanical work, thus changing the total energy, therefore it is false.