Respuesta :
Answer:
a. 10kg/m
b. 40kg/m
c. 50kg/m
Explanation:
Linear density is the measurement of a quantity of any characteristic value per unit of length. Linear mass density in engineering, the amount of mass per unit length and linear charge density is referred to as the amount of electric charge per unit length) are two common examples used in science and engineering.
Linear density is often times used to describe the characteristics of one-dimensional objects, however, linear density can also be used to describe the density of a three-dimensional quantity along one particular dimension.
The mass part of the metal rod lies between its left end and a point x meter to the right is 5x^2
So the linear density is given by:
dS/dy= 5(2x)= 10x
a) When x is 1m, the linear density is:
10(1)= 10kg/m
b) When x is 4m, the linear density is:
10(4)= 40kg/m
c) When x is 5m, the linear density is:
10(5)= 50kg/m
Since density function is a linear function, the density is highest at the right end of the rod and lowest at the left end of the rod.
Answer:
a) 10 kg/m
b) 40 kg/m
c) 50 kg/m
Density will be highest at right end of the rod and lowest at left end of the rod.
Explanation:
Formula to calculate linear density is the derivative of mass with respect to x (position).
Linear Density = dm/dx
So, here we have mass = m = 5[tex]x^{2}[/tex]. In order to calculate linear density just take the derivative of this mass function with respect to x and then plug in the value of x in that derivative.
Solution:
1. m = 5[tex]x^{2}[/tex] , x = 1
Linear Density = dm/dx = d5[tex]x^{2}[/tex]/dx = (5*2)x = 10x
Linear Density = 10x
Now, plug in the value of x in this function to get the numerical value of linear density.
Linear Density = 10*(1) = 10 kg/m
2. when x = 4,
Similarly, plug the value of x in the obtained function
Linear Density = 10x = 10 (4) = 40 kg/m
3. When x = 5,
Linear Density = 10x = 10*(5) = 50 kg/m.
Density will be highest at right end of the rod and lowest at left end of the rod as seen from the equation of linear density that it is proportional to x which is position and it is increasing to the right and decreasing to the left. Hence, density will be highest on right end and lowest on left end.
