Engineering Mechanics Questions and Answers

Q.1 ) A aircraft takes off from a runway and and then turns northwest at 30^o and goes for 10km and then take a left turn of 10^o  and goes for 12km and then goes to south for about 3km  and then goes to south-east for 15 km and then goes north for 3 km and then again goes to southeast for 6 kms and then goes to west for 2km and then goes to north-east for 20km and then at last makes a left turn of 135^o and goes for 30 km and reaches its destination

a) Find total distance in metre, miles ,ft

(Ans :  101km,101000m,62.75 mil,331364.829 ft)

b) Find displacement in Kilometre, metre, miles and in ft.

(Ans :  20.181km, 20181m, 12.539miles, 66210.629 ft)

Q.2) A rocket is ready for launching it is divided into three parts

·       Bottom part consist of 2000 metric tons

·       Fuel chamber consisit of 50,000 kg fuel

·       Top part consist of 1500 tons.

The maximum strength of a rocket is 5g and we want to cover a distance of 10,000 miles

a)    Total mass in Kg and metric tons.

(Ans :3550 tons, 3550000 kg)

b)    Total time required to cover a given distance

(Ans : 810.478 sec)

c)     Find minimum force required to lift the rocket from the ground

(Ans : 34790000N)

d)    Find the force of a given Acceleration

(Ans: 208740000N)

Q.3) Find the load of bulding consist of 3 floors each floor have following appliences

·       Tube light = 40 watts

·       Fan =150 watts

·       A/C = 2.5 kwatts

·       Fridge = 300 watts

·       Computer = 250 watts

·       Laptop = 150 watts

·       Savers = 22 watts

·       TV = 350 watts

First floor  have

·       10 =Tube light

·       6 = Fan

·       3 = A/C

·       2 = Fridge

·       15 = Computer

·       3 = Laptop

·       20 = Savers

·       2 = TV

(Total = 14740 watts)

Second floor  have

·       15 =Tube light

·       9 = Fan

·       4 = A/C

·       2 = Fridge

·       20 = Computer

·       3 = Laptop

·       25 = Savers

·       1 = TV

(Total = 18900 watts)

Third Floor

·       25 =Tube light

·       12 = Fan

·       6 = A/C

·       3 = Fridge

·       24 = Computer

·       2 = Laptop

·       26 = Savers

·       4 = TV

(Total = 26972 watts)

a)    Calculate Total Power for each floor (Answer is above)

b)    Calculate Total power of Building (Ans : 60.612Kw)

c)     Calculate Total energy for Office hours 9 to 5 (6 days a week)

(Ans : Monthly 11637.504 kw , Weekly : 2909.376 Kw)

d)    Calculate Weekly price And Monthly price at =  9 Rs/Kw

(Ans : Monthly 104737.53 Rs , Weekly : 26184.384 Rs)

Q.4 Mass calculate of given material p= 8500kg/m³ and price pr kg is 80rs

(Ans : Mass = 7.2408 kg , 579.2716 Rs )

Q.5 A Person have a average mass of 75 kg and he is on the inclined plane of 35^O

And coming down with  a 55 kg trolley  full of apples of about 150kg and suddenly when he at a distance of 100m left from the straight ground a trolley slips form his hands and now trolley and apples are freely moving towards a ground.

·       Find the acceleration and also time it takes to reach the ground.

(Ans : a= 5.62m/s² , t = 5.964 or 6 sec)

·       Find the acceleration if the body is freely falling and find how mush time it takes to reach the ground.

(Ans : a=9.8 , t=3.421sec       100% correct  )

·       Also Find the force of a trolley and apples at an inclined plane and also find the its weight.

( Ans : F = 1152.315 N  ,  W = 2009 N)

·       And if the trolley didn’t slip from a persons hands and he is coming down with a acceleration of 6km/h then how much time its takes to reach the ground

(Ans : a = 1.66m/s²  ,t = 10.956 or 11 sec)

Q.6 Find I,j,k and its magnitude and also find a unit vector ,also find alpha beta, gamma (Sorry 4 m is wrongly printed neglect 4 m In this question then solve it again)

(Ans : 4.59i + 3.856j + 3.217k

Magnitude = 6.808

Unit vector= 0.6751i +0.5664j +0.4725k

α)47.53^o

β) 55.5004^o

Gamma ) 61.803^o

Cos(alpha)²+cos(beta)²+cos(gamma)²=1 Proved )

Q.6 ) A (6,2,-2), B(4,1,-7), C(8,-4,-2) , D (1,-4,-7) , E(-2,10,-6)

Find resultant vector and alpha, beta , gamma .

(Ans : 8i – 8j + 4k , Magnitude = 12 units, Alpha = 48.189 ,beta = 131.8103 , Gamma = 70.5287)

Find distance traveled.

(Ans : 36.55 units )

Q.7 ) A car of 1500 kg is at a height of 20m with velocity of 20km/h and comes down to ground and at ground its velocity is 45km/h and after covering some distance  and gain a speed of 80km/h and then it again goes to a height of 60m and at that time its velocity is 25km/h
a) finds its net energy.

(Ans : 1211416.65 Joules)
b) when car is at ground how much potential energy a car gains during this interval. Explain it with justifications  (Ans :  Car doesn’t gain any Energy because on ground our height is zero with respect to ground )