Engineering Studies Formulas Quiz

What is the formula for efficiency (η) in terms of mechanical advantage (MA) and velocity ratio (VR)?

• η = MA/VR

• η = VR/MA

• η = MA + VR

• η = MA - VR

Answer explanation

The formula for efficiency (η) is defined as the ratio of mechanical advantage (MA) to velocity ratio (VR). Thus, the correct choice is η = MA/VR, indicating how effectively a machine converts input work to output work.

What is the formula for mechanical advantage (MA) in terms of load (L) and effort (E)?

• MA = L/E

• MA = E/L

• MA = L + E

• MA = L - E

Answer explanation

The formula for mechanical advantage (MA) is defined as the ratio of load (L) to effort (E). Therefore, the correct choice is MA = L/E, which indicates how much the machine amplifies the input force.

What is the formula for the moment (M) in terms of force (F) and distance (d)?

• M = Fd

• M = F/d

• M = F + d

• M = F - d

Answer explanation

The moment (M) is calculated by multiplying the force (F) applied to an object by the distance (d) from the pivot point. Therefore, the correct formula is M = Fd.

What is the formula for frictional force (F) in terms of the coefficient of friction (μ) and normal force (N)?

• F = μN

• F = μ/N

• F = N/μ

• F = μ + N

Answer explanation

The formula for frictional force (F) is given by F = μN, where μ is the coefficient of friction and N is the normal force. This relationship shows that frictional force is directly proportional to both the coefficient of friction and the normal force.

What is the formula for allowable stress (σ_allowable) for ductile materials?

• σ_allowable = σ_yield/F of S

• σ_allowable = σ_UTS/F of S

• σ_allowable = F of S/σ_yield

• σ_allowable = F of S/σ_UTS

Answer explanation

The allowable stress (σ_allowable) for ductile materials is calculated using the yield strength (σ_yield) divided by the factor of safety (F of S). This ensures that the material remains within safe limits under load.

The pressure at depth h in the liquid can be calculated using which equation?

• P = P0 + ρgh

• P = ρg + h

• P = P0 - ρgh

• P = ρg/h

Answer explanation

The correct equation for calculating pressure at depth h in a liquid is P = P0 + ρgh, where P0 is the atmospheric pressure, ρ is the liquid density, and g is the acceleration due to gravity.

What is the formula for electrical energy (E) in terms of current (I) and resistance (R)?

• E = IR

• E = I/R

• E = R/I

Answer explanation

The correct formula for electrical energy (E) in terms of current (I) and resistance (R) is E = I^2R. This shows that energy is proportional to the square of the current multiplied by resistance, not E = IR.

What is the formula for kinetic energy (KE)?

• KE = mgh

• KE = Fs

Answer explanation

The correct formula for kinetic energy (KE) is KE = \frac{1}{2} mv^2, where m is mass and v is velocity. This formula shows that kinetic energy is proportional to the mass and the square of the velocity of an object.

What is the formula for change in potential energy (ΔPE) in terms of work (W) and change in kinetic energy (ΔKE)?

• W = ΔPE + ΔKE

• W = ΔPE - ΔKE

• W = ΔPE * ΔKE

• W = ΔPE/ΔKE

Answer explanation

The work done (W) on an object is equal to the change in potential energy (ΔPE) plus the change in kinetic energy (ΔKE). This relationship is derived from the work-energy principle, making W = ΔPE + ΔKE the correct choice.

What is the formula for allowable stress (σ_allowable) for brittle materials?

• σ_allowable = σ_UTS/F of S

• σ_allowable = σ_yield/F of S

• σ_allowable = F of S/σ_yield

• σ_allowable = F of S/σ_UTS

Answer explanation

The allowable stress for brittle materials is calculated using the ultimate tensile strength (σ_UTS) divided by the factor of safety (F of S). Thus, the correct formula is σ_allowable = σ_UTS/F of S.