Motion of the boat, Mechanical Engineering

Motion of the boat:

 (i) A man having weighs 500 N and is in a boat weighing 1500 N which is free to move over a steady lake. If he begins running along the length of the boat at a speed of 4 metres/second with respect to the boat-floor, supposing that there is no resistance of water to the motion of the boat, find out the velocity of the boat.

 (ii) Then if he jumps over the boat and absolute velocity of 6 metres/seconds, then what would be the motion of the boat?

Solution

 (i) As both man and the boat are initially at rest, the initial total-momentum is zero. Therefore by the principle of conservation of momentum, the total momentum for this system shall be zero at any other time. If the velocity of man is Vm/b with respect to the floor of the boat along x direction, let Vb be the absolute velocity of the boat developed due to the interaction developed.

The absolute (or true/actual) velocity of the man Vm is, thus, equal to (Vm/b  + Vb ) . The equation of conservation of momentum is associated with masses mb and mm of the boat and the man, respectively.

∴ mb  (Vb ) + mm  (Vm ) = 0

(1500/9.8) (V ) +( 500/9.8) (V m/b + V b ) = 0

∴ Vb  (1500 + 500) = - Vm/b  × (500)

∴ (Vb ) = - (4 × 500) /2000

          = - 1 m / sec

Therefore, the boat moves with a velocity of 1 m/sec in negative x direction and true (absolute) velocity of man reduces.

               Actual (Absolute) velocity of man = Vm/b  + Vb

                                                                       = 4 - 1 = 3 m / sec.

 (ii) While the man jumps out of the boat with absolute velocity Vm′ = 6 m / sec, the boat shall attain a velocity Vb′ whereby,

                               mb  (Vb′) + ( mm ) Vm′ = 0

                                 ∴ (1500/9.8) × V b′ = - (500 /9.8) × 6

                                ∴ Vb′ = - 2 metres / sec.

Negative sign again indicates that velocity (Vb′) of the boat has direction opposite to the direction of the man's jump.

Posted Date: 1/29/2013 6:52:40 AM | Location : United States







Related Discussions:- Motion of the boat, Assignment Help, Ask Question on Motion of the boat, Get Answer, Expert's Help, Motion of the boat Discussions

Write discussion on Motion of the boat
Your posts are moderated
Related Questions
It is a 3-D drawing used by draftsmen, architects etc

Quasi static process - thermodynamics: Thermodynamic equilibrium of a system is very difficult to be realized during the occurrence of a thermodynamic process. 'Quasi-static'

Calculate stress to cause failure - Creep Parameters: From creep tests on 713 C alloy the constant C in Larson-Miller parameter is determined as - 85.75. In rupture test a spe

Solve the support reactions at A and D by using the force method. A is a fixed support; B and C are rigid joints; and D is a pin support. EI is constant for all members.

A cantilever beam of 1800 mm length is subjected to point loads of 3.5 kN, 4.3 kN, 1.2 kN and 2.8 kN at distances of 400 m, 400 m, 400 m 300 m and 300 m, respectively from the fixe

Axi s of symmetry If in diagram half part of diagram is mirror image of next ½ part, then there is a symmetry in diagram. The axis at which symmetry is create, called as axis

Inspection of Electrical Equipment STEPS All electrical equipment are checked for proper functioning. The starting and lighting of the motorcycle should be prope

how is varignons theorem useful in engineering mechanics

i have an assignment due tomorrow

computer aided design of piercing press tool