Tutorial Unit 4 1 Kinematics

(R20080902S)

KALI CHARAN NIGAM INSTITUTE OF TECHNOLOGY, BANDA B.Tech. I Year

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TUTORIAL SHEET  – UNIT-4-1

EME-102 / 202 : Engineering Mechanics

The distance between two stations is 3.6 m. A train starting from one station, receives an acceleration( reaching a speed of 6.0 m /s in 5 seconds) until the speed reaches 12 m/s. This speed speed is maintained until the brakes are applied and train is brought to rest at the second station under a negative acceleration of 1.5 m/s2, find the time to perform this  journey . Two trains A and B leave the same station on parallel lines. A start with uniform acceleration of 0.15 m/s 2 and attains a speed of 27 km/hour . When steam is reduced to keep the speed constant . B leaves 40 seconds after with a uniform acceleration of 0.3 m/s 2 to attain a maximum speed of 54 km/hr. When and where will B overtake A ? A ball is dropped from the top of a tower 30 m high. At the same instant a second ball is thrown upward from the ground with an initial velocity of 15 m/s. When and where do they cross and with what relative velocity. A stone is dropped into a well and sound of splash is heard on the top after 4 seconds. If the sound travels at 340 m/s determine the depth of the well. The position of a particle moving along a straight line is defined by the relation x = t3 – 9 t 2 + 15 t + 18 where x is expressed in metres and t in seconds. Determine the time, position and acceleration of the particle when its velocity becomes zero. A wheel rotates for 5 seconds with a constant angular acceleration and describes during this time 120 radians. It then rotates with constant angular velocity, and during the next 5 seconds describes 100 radians. Find the initial angular velocity and the angular acceleration. A motorist motorist is driving his car at 40 km/hr. He observes observes red light 200 m ahead turn ahead turn red. The traffic traffic light remain red for for 15 second.

Compiled By RAKESH SRIVASTAVA, Associate Professor & Dean KCNIT, Banda

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If the motorist wishes to pass the light without stopping, find the required minimum acceleration. (UPTU Second Semester Exam. 2000-2001) 

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A train starts from rest and moves along a curved track of radius 800 m with a uniform acceleration until it attains a velocity of 72 km/hr at the end of third minute. Determine the tangential, normal and total acceleration in m/s2 of the train at the end of second minute. (UPTU Second Semester Exam. 2000-2001) 

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A cylinder of radius 1 m rolls without slipping along a horizontal plane AB. Its center has a uniform velocity of 20 m/s. Find the velocity of points E and F on the circumference of the cylinder shown in fig.

(UPTU First Semester Exam. 2001-2002)  10

3   arctan  4  to

A girl hits a ball at an angle the horizontal from a point O which is 0.5m 1 above level ground. The initial speed of the ball is 15ms . The ball just clears a fence which is a horizontal distance of 18m from the girl. By modelling the ball as a particle find the time taken for the ball to reach the fence and the height of the fence.

(R20080902S) Compiled By RAKESH SRIVASTAVA, Associate Professor & Dean KCNIT, Banda

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KALI CHARAN NIGAM INSTITUTE OF TECHNOLOGY, BANDA TUTORIAL SHEET  – UNIT-4-1

B.Tech. I Year

EME-102 / 202 : Engineering Mechanics

ANSWERS Q.No. Q.1. [309 s]

HINTS

ANSWERS

Make v-t graph

Q.2.

[105 s, 600m]

t is same

Q.3.

[t = 2 second, 10.38 m from the ground, Relative velocity= 15 m/s]

Use equations of motion

Q.4.

No effect of gravity on sound

[70.54 m]

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Q.5.

[ t = 1, x = 25 cm, a = -12 m/s ] 2 [ t = 5, x = -7m, a = 12 m/s ]

Q.6.

[

Q.7. Q.8. Q.9

a= - 1.56 m/s 2 2 2 aT=0.1112 m/s , aN=0.223 m/s , a=0.250 m/s , VE= 20√2 m/s VF=40 m/s

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= 28 rad./s.,

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= -1.6 rad./s .]

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Put dv/dx=0

Use equations of motion Use equations of motion Instantaneous centre theory Projectile motion

Q.10

Fence height = 2.96m,

t=1.5 sec.

Compiled By RAKESH SRIVASTAVA, Associate Professor & Dean KCNIT, Banda

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