Answer:
The correct answer is "64 J".
Explanation:
The given values are:
Mass,
m = 52 kg
Velocity,
v = 6 m/s
Mechanical energy,
= 1000 J
Now,
The gravitational potential energy will be:
⇒ 




Answer:
a)
, b) 
Explanation:
The magnitude of torque is a form of moment, that is, a product of force and lever arm (distance), and force is the product of mass and acceleration for rotating systems with constant mass. That is:



Where
is the angular acceleration, which is constant as torque is constant. Angular deceleration experimented by the unpowered flywheel is:


Now, angular velocities of the unpowered flywheel at 50 seconds and 100 seconds are, respectively:
a) t = 50 s.


b) t = 100 s.
Given that friction is of reactive nature. Frictional torque works on the unpowered flywheel until angular velocity is reduced to zero, whose instant is:


Since
, then the angular velocity is equal to zero. Therefore:

Answer:
Vf = - 20 m/s ( -ve sign shows that the particle is moving opposite to positive x- direction).
Explanation:
Given:
Vi = 20 m/s, m= 10 mg =1 × 10⁻⁵ kg, q= -4.0 × 10⁻⁶ C , E= 20 N/C. t= 5.0 s
first to find Electric Force
F= Eq = 20 × -4.0 10⁻⁶ C = - 8 × 10⁻⁵ N (-ve sign shows that the field will push the particle opposite to positive x- direction)
We also have F=ma
⇒ a = F/m = - 8 × 10⁻⁵ N / 10 × 10⁻⁵ kg = -8 m/s² ( -ve sign shows that the particle is accelerated opposite to positive x- direction)
Now according the first equation of Motion.
Vf = Vi + at
Vf = 20 m/s + -8 m/s² × 5 s
Vf= -20 m/s ( -ve sign shows that the particle is moving opposite to positive x- direction)
Answer:
same value in R and 2R E = E₀ = σ / 2ε₀
Explanation:
For this exercise we use Gauss's law
Ф = E. dA =
/ε₀
We define a Gaussian surface with a cylinder with the base being parallel to the load sheet, so the electic field line and the normal line to the base are parallel and the scalar product is reduced to the algebraic product, in the parts the angle is 90º and the dot product is zero
As the sheet has two faces
2E A = q_{int} /ε₀
The charge inside the cylinder is
σ = q_{int} / A
q_{int} = σ A
We substitute
E = σ / 2ε₀
We see that this expression is independent of the distance, so it has the same value in R and 2R
E = E₀ = σ / 2ε₀