A single mass m1 = 4.1 kg hangs from a spring in a motionless elevator. The spring is extended x = 13 cm from its unstretched le
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The work done onto the car is 506,250 J
The work done on a system implies an increase in the internal energy of the system as a result of some forces acting on the system from the outside.
From the parameters given:
- The mass of the car = 1500 kg
- The initial speed = 30 m/s
- The final speed = 15 m/s
The work done onto the car refers to the change in the kinetic energy (i.e. ΔK.E)
= 506,250 J
Therefore, we can conclude that the work done on the car is 506,250 J
Learn more about work done here:
Hi there!
a)
We can begin by using the equation for energy density.
U = Energy (J)
ε₀ = permittivity of free space
E = electric field (V/m)
First, derive the equation for the electric field using Gauss's Law:
Creating a Gaussian surface being the lateral surface area of a cylinder:
Now, we can calculate the energy density using the equation:
Plug in the expression for the electric field and solve.
b)
Now, we can integrate over the volume with respect to the radius.
Recall:
Now, we can take the integral of the above expression. Let: = inner cylinder radius
= outer cylindrical shell inner radius
Total energy-field energy:
Plug in the equation for the electric field energy density and solve.
Bring constants in front and integrate. Recall the following integration rule:
Now, we can solve!
To find the total electric field energy per unit length, we can simply divide by the length, 'L'.
And here's our equation!