Test: Work and Energy Principle - Civil Engineering (CE) MCQ

Since we are equating work done, it compulsory for them to be in equilibrium.

External and internal displacements must be related by compatibility of displacement.

It is required for structure to be stable for application of this method.

As after elastic limit, work done can’t be equated.

In these cases, each one has unique relationship between load and deformation.

In these cases, both are directly proportional.

In cases of dynamic load, acceleration may occur and some of the external work will be transferred into kinetic energy.

They are equal only when Hooke’s law is applicable i.e. the material is linearly elastic.

Work  done = Force applied × Displacement 
Calculation
Here 10 kg block will be displaced by 20m hence work done displace bucket by 20 meters = 10 × 20 = 200 kg-m and the total weight of rope mass per unit length ×  length = 1 × 20 = 20kg and it will be concentrated at the center of the rope hence net displacement of rope = 10m, therefore, work done to displace rope 20 × 10 = 200 kg-m
Hence net work done  = 200 + 200 = 400 kg-m

Non-conservative forces:

• A non-conservative force is one for which work depends on the path taken.
• Friction is an example of a non-conservative force that changes mechanical energy into thermal energy.
• Work W_nc done by a non-conservative force changes the mechanical energy of a system.
• In equation form, W_nc = ΔKE + ΔPE or, equivalently, KE_i + PE_i = W_nc + KE_f + PE_f.

Conservative forces:

• A conservative force is one, for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. 
• Example potential energy, gravitational force etc.
• Work done by conservative force is equal to decrease in potential energy.