Find out nature of position vector, Mechanical Engineering

Find out nature of position vector:

The position vector of a specific at any instant t with respect to the axes x, y and z is specified by

r (t ) = (4 t 2  + 5) i¯ + (3 t 2  + 2)j¯ + 0 k¯

Find out nature of its path and its position, velocity and acceleration at t = 3 seconds. Distances are measured in centimeters.

Solution         

As the coefficient of k in the given equation is zero, there is no displacement along z direction at any time t. This may be described as a motion of a particle in plane (XOY). If there is any coefficient for the k vector of the motion, the motion of the particle shall be in space.

The given equation of motion can be written as

x (t ) = 4 t 2  + 5,

y (t) = 3 t 2  + 2

 Eliminating t2 from the above two relations, we obtain

t 2  = x - 5/4  = y - 2 / 3

∴ 3 x - 15 = 4 y - 8

∴ 3 x - 4 y - 7 = 0

The velocity and acceleration of the particle may be calculated from the relations

dx/ dt =  d /dt (4 t+ 5) = 8 t,             dy / dt =  d dt  (3 t 2  + 2) = 6 t

d 2 x / dt 2  = 8,     d 2 y/ dt 2 = 6t

at         t = 3     v = 24 i¯ + 18 j¯

= 30 cm / sec. (that means723_Find out nature of position vector.png)

a = 8 i¯ + 6 j¯

= 10 cm / sec 2 .

Posted Date: 1/29/2013 1:44:25 AM | Location : United States







Related Discussions:- Find out nature of position vector, Assignment Help, Ask Question on Find out nature of position vector, Get Answer, Expert's Help, Find out nature of position vector Discussions

Write discussion on Find out nature of position vector
Your posts are moderated
Related Questions
A load of 2MN is applied on a short concrete column 500 mm x 500 mm. The column is reinforced with four steel bars of 10 mm diameter, one in each corner. Evaluate the stresses in t

What do you mean by Heat Transfer ? Compare (i) Work done with Heat Transfer (ii) Thermodynamics with Heat Transfer. State whether Heat Transfer is a path function or state functio

can we use electrical power chuck for job clamping in cnc lathe.what are the issues related

The Bronzes The coinage bronze employed for making coins in earlier days contains 95% copper, 4% Sn and 1 % Zn. The Zn acts as a deoxidizer. Such alloy is soft and ductile.

What is the clear difference between gravitational potential and gravitational potential energy ? Ans) A body A of mass m is placed in the gravitational field of a body B of mass

Explain the Application of Electro Chemical Machining? 1. EBM has been used to perforate holes in glass fiber spinning head made from a heat resistant supper alloy. 2. Slott

A steel tube of 30 mm external diameter and 20mm internal diameter encloses a copper rod of 15mm diameter to which it is rigidly joined at each end. If at a temperature of 10 o C,

Maximum shear stress and angle of twist: Torques are applied on the shaft as illustrated in Figure. Discover in which portion of the shaft, maximum shear stress & angle of twi


when correction couple should be applied?