Engineering Mechanics Problem Sheet – 1 Module - 1 ...



Part A -Rectilinear motion (Uniform Acceleration)

1. What leaks from the ceiling 16m high, at the rate of 5 drops per second. Find the distance between first and the second drop when first drop has just touched the ground. Dec 2007 (5 marks)

[pic] Ans: d=3.347m t1= 1.8061(s),t2=1.6061(s),y2=12.65m, CB=3.347m

2. A stone is released from top of a tower. During the last second of its motion it covers 1/4th of the height of the tower find the height of the tower. Dec 2008 (5marks)

[pic] Ans: h=273.26

3. A stone is dropped from the top of a tower. When it has fallen a distance of10m, another stone is dropped from a point 38m below the top of the tower. If both the stones reach the ground at the same time calculate: Dec 2009 (10marks)

i) The height of the tower.

ii) The velocities of the stones when they reach the ground.

[pic] Ans: H=57.63m , Ans: V1=33.63, V2=19.62 m/s

4. In an Asian games event an athlete accelerates uniformly from the start to his maximum velocity in a distance of 4m and runs the remaining distance with that velocity. If the athlete completes the race in 10.4 seconds, determine his initial acceleration and his maximum velocity. May 2011 (5 marks)

Ans: Vmax= 10m/s, a=12.5m/s2

5. A stone is thrown vertically upwards and returns to the starting point at the ground in 6 sec. find out maximum height and initial velocity of stone. May 2013(6 marks)

Ans: h=44.145m

PART B-Variable Acceleration (Rectilinear Motion)

6. Acceleration of particle is directly proportional to the square of time ‘t’. when t=0,particle is at x=24m.knowing that at t=6sec,x=96m and v=18m/s.Find expressions of x and V in terms of t. also find velocity and position at t=2sec. Dec 2007 (10 marks)

Ans: x=44.148m, v= 10.3m/s

7. The motion of a particle moving in a straight line is given by the expression s=t3-3t2+2t+5 where s is the displacement in meters and ‘t’ is time in seconds. May 2009, (8 marks)

Determine:

i) Velocity and acceleration after 4 seconds . Ans: V=26m/s, a=18m/s2

ii) Maximum or minimum velocity and corresponding displacement v= -1m/s, s=5m

iii) Time at which velocity is zero. t=1.577(S)

8. The acceleration of the particle is defined by the relation a=25-3x2mm/s2. The particle starts with no initial velocity at the position x=0. (a) Determine the velocity when x=2mm. (b) The position when velocity is again zero. (c) Position where the velocity is maximum and the corresponding maximum velocity. Dec 2010(8marks)

Ans: V=±9.165mm/sec, x=±5mm, x=2.886mm, v=9.81mm/sec

9. During a test, the car moves in a straight line such that its velocity is defined by v=0.3(9t2+2t)m/s, where ‘t’ is in seconds. Determine the position and acceleration when t=3sec. take at t=0,x=0. May 2012(5marks)

Ans: a=16.8m/s2, X=27m

10. A particle moving in the +ve X direction has an acceleration a=100-4v2 m/s2. Determine the time interval and displacement of a particle when speed changes from 1m/s to 3m/s. Dec 2012(4marks)

Ans: a=16.8m/s2, x=27m

11. For a particle in rectilinear motion a=-0.05V2m/s2, at v=20m/s,X=0. Find X at V=15m/s and acceleration at x=50m. May 2013(4marks)

Ans: X=5.754m, a==0.1345 m/s2

Part C-Motion diagrams

12. The race car starts from rest and travels along a straight road until it reaches a speed of 42m/s in 50 seconds as shown by v-t graph. Determine the distance travelled by race car in 50 seconds. Draw x-t and a-t graph. May 2008 (10 marks)

[pic] d=960m

13. Figure shows an plot of ax versus time for a particle moving along x-axis. What is the speed and distance covered by the particle after 50 seconds? May 2010 (5marks)

[pic] Ans: t= 50(s), x= 15000m

14. A Car moves along a straight road such that its velocity is described by the graph shown in fig. For the first 10 seconds the velocity variation is parabolic and between 10 seconds to 30 seconds the variation is linear. Construct s-t and a-t graphs for the time period 0 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download