Answer:
a. dW = ∫pEsinθdθ b. W = p.E
Explanation:
a. We know torque τ = p × E = pEsinθ where θ is the angle between p and E
Let the torque τ rotate the dipole by an amount dθ. So, the workdone dW = ∫τdθ = ∫pEsinθdθ
b. So, the total work done is gotten by integrating from 90 to θ. So,
W = ∫₉₀⁰dW
= ∫₉₀⁰pEsinθdθ
= pE∫₉₀⁰sinθdθ
= pE(cosθ - cos90)
=pEcosθ
= p.E
Answer:2.5 m/s
37.5KJ
Explanation:
Let 
be the initial velocity of rail road car ,coupled cars & Final velocity of system respectively.
Conserving momentum
Therefore Final velocity of system is 2.5m/s
(b)Mechanical Energy lost =Initial Kinetic Energy -Final Kinetic Energy
Answer:
the energy required for the extension is 12.25 J
Explanation:
Given;
force constant of trampoline spring, k = 800 N/m
extension of trampoline spring, x = 17.5 cm = 0.175 m
The energy required for the extension is calculated as;
E = ¹/₂kx²
E = 0.5 x 800 x 0.175²
E = 12.25 J
Therefore, the energy required for the extension is 12.25 J
a)You throw a stone horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high.
from above statement we got
height = 78.4 m
since the ball is thrown, so its vertical velocity would be zero
u = 0
taking g = 9.8m/s^2
now, using the equation of motion
h = ut + gt^2/2
now putting all the values in it
we got ,
78.4 = 9.8 * t^2/ 2
by solving we got,
t = 4 sec
b) now, since along the horizontal , no force acting and accelaration is zero so
R = ut , R is RANGE
R = 5 * 4
range = 20 m
c) vertical components of the stone’s velocity just before it hits the ground = v sin θ =
horizontal components of the stone’s velocity just before it hits the ground = v cos θ
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