Solution Library


Physics


Calculation of Maximum Distance Up an Inclined Plane

Question   The maximum distance up an inclined plane (of an inclination 𝛼𝛼) reached by an object of mass m, taking the air resistance proportional to the instantaneous velocity (constant of proportionality K) into account is a) Find the inclination 𝛼𝛼 of the p ... Read More

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Calculation of Time to Reach Maximum Height by Projection

Question   An object is projected vertically upward from the earth’s surface with an initial velocity 𝑣𝑣0 of magnitude less than the escape velocity. If the earth’s influence is taken into account, the time for the projectile to reach the maximum height is a) Show ... Read More

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Calculation of Speed of an Object Falling from Center of the Earth

Question     Summary This question belongs to Mechanics and discusses about calculation of Speed of an Object Falling from Center of the Earth. ... Read More

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Initial Velocity of the Rocket if it Reaches a Maximum Height

Question   From the immemorial, mankind has gazed at the moon, wondering about many things, one of them being whether a day might come when men could be there.Following the Newton’s law of universal gravitation which shows the possibility of firing a projectile (rocket) out of the earth ... Read More

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Calculation of Radius of Plastic Front Using Newton-Raphson's Method

Question   At the last conference of Nigeria Society of Engineers (NSE), a mechanical engineer presented a paper on the “Effects of Noise on Machine Operator”. In the work, he developed a mathematical model using Taylor’s series and carried out all the computations to four d ... Read More

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Relationship Between Force and Wind Velocity in a Wind Tunnel

Question   Fig. Q1 shows a wind tunnel with a suspended object. The force measured for various levels of wind velocity are given in the Table below.     Summary This question belongs to Mechanics and discusses about relationship between the force and the wind velocity.   ... Read More

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Solving Nozzle Flow Equation Using Newton Raphson's Method

Question   Solve equation  using Newton-Raphson’s method. Construct a table of M vs 𝛿𝛿 for 𝛾𝛾=1.4 and 𝑀 1=1.0, for 0≤δ≤40𝑑𝑑𝑑𝑑 𝑑, in increments Δ𝛿𝛿=1.0𝑠... Read More

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Calculation of Specific Volume Using Van Der Waal Equation

Question   The van der Waal equation of state for a vapor is Where P is the pressure (Pa = N/m2), v is the specific volume (m3/kg), T is the temperature (K), R is the gas constant (J/kg-K), and a and b are empirical constants. Consider water vapor, for which R = 461.495 J/kg-K, a = 1703.28 ... Read More

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Solving F Value for a Pipe Using Colebrook Equation

Question   When an incompressible fluid flows steadily through a round pipe, the pressure drop due to the effects of wall friction is given by the empirical formula:   Summary This question belongs to Mechanics and discusses about determining f for a pipe using Colebrook equation. ... Read More

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Value of M of a Isentropic Flow of a Perfect Gas by Newton's Method

Question   Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable-area channel. The relationship between the Mach number M and the flow area A, derived by Zucrow and Hoffman [1976, Eq. (4.29)], is given by where 𝐴𝐴∗ is the choking area (i.e. ... Read More

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Isentropic Supersonic Flow Around a Sharp Expansion Corner

Question   Consider isentropic supersonic flow around a sharp expansion corner. The relationship between the Mach number before the corner (i.e., M1) and after the corner (i.e., M2), derived by Zucrow and Hoffman [1976] is given by where 𝑏𝑏=(𝛾𝛾+1)/(𝛾 ... Read More

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Calculation of Capacitor Charge

Question   An emf of 𝐸𝐸0𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐 volts, where 𝐸𝐸0,𝜔 are constants, is applied at t = 0 to a series circuit consisting of R ohms and C farad where R and C are constant. If Q = 0 at t = 0 and at ... Read More

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