Answer:
false statement : b ) For the motion of a cart on an incline plane having a coefficient of kinetic friction of 0.5, the magnitude of the change in kinetic energy equals the magnitude of the change in gravitational potential energy
Explanation:
mechanical energy = potential energy + kinetic energy = constant
differentiating both side
Δ potential energy + Δ kinetic energy = 0
Δ potential energy = - Δ kinetic energy
first statement is true.
Friction is a non conservative force so inter-conversion of potential and kinetic energy is not possible in that case. In case of second option, the correct relation is as follows
change in gravitational potential energy = change in kinetic energy + work done against friction .
So given 2 nd option is incorrect.
In case of no change in gravitational energy , work done is equal to
change in kinetic energy.
Answer:
Given:
Thermal Kinetic Energy of an electron, 
= Boltzmann's constant
Temperature, T = 1800 K
Solution:
Now, to calculate the de-Broglie wavelength of the electron,
:

(1)
where
h = Planck's constant = 
= momentum of an electron
= velocity of an electron
= mass of electon
Now,
Kinetic energy of an electron = thermal kinetic energy



(2)
Using eqn (2) in (1):

Now, to calculate the de-Broglie wavelength of proton,
:

(3)
where
= mass of proton
= velocity of an proton
Now,
Kinetic energy of a proton = thermal kinetic energy



(4)
Using eqn (4) in (3):

The height above the ground from where the skier start is 11.5 m.
<h3>
Conservation of energy</h3>
The height above the ground from where the skier start is determined by applying the principle of conservation of energy as shown below;
P.E = K.E
mgh = ¹/₂mv²
gh = ¹/₂v²

Thus, the height above the ground from where the skier start is 11.5 m.
Learn more about conservation of energy here: brainly.com/question/166559
Answer
given,
vertical speed of stone,v = 12 m/s
height of the cliff = 70 m
a) time taken by the stone to reach at the bottom of the cliff
We know that,
S = u t + 1/2 a t²
- 70 = 12 t - 0.5 x 9.8 t²
4.9 t² - 12 t - 70 = 0
solving the equation
t = 5.2 s (neglecting the negative value)
b) again using equation of motion
v = u + a t
v = 12 - 9.8 x 5.2
v = -38.96 m/s
ignoring the negative sign
magnitude of velocity is equal to 38.96 m/s
c) total distance travel by the stone
vertical distance covered by the stone
v² = u² + 2 g h
0 = 12² - 2 x 9.8 x h
h = 7.34 m
to reach the stone to the same level distance travel be doubled.
Total distance travel by the stone
H = h + h + 70
H = 7.34 x 2 + 70
H = 84.7 m.