A ball is launched with initial speed v from ground level up a frictionless slope (This means the ball slides up the slope witho
1 answer:
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Answer:195 J
Explanation:
Given
mass of ball
ball leaves the hand with
maximum height reached by ball
Initial Mechanical energy when ball just leaves the hand
considering hand to be datum so h_1=0[/tex]
so Potential energy at ground is zero
Mechanical Energy at highest point
at highest Point velocity is zero
Decrease in Mechanical energy
Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
Answer:
(a) momentum of photon is 1.205 x 10⁻²⁷ kgm/s
velocity of electron is 1323.88 m/s
momentum of the electron is 1.205 x 10⁻²⁷ kgm/s
(b) momentum of photon is 1.506 x 10⁻²⁷ kgm/s
velocity of electron is 1654.85 m/s
momentum of the electron is 1.506 x 10⁻²⁷ kgm/s
(c) The momentum of the photon is equal to the momentum of the electron
Explanation:
(a)
wavelength of green light, λ = 550 nm
momentum of photon is given by;
velocity of electron is given by;
momentum of the electron is given by;
p = mv
p = (9.1 x 10⁻³¹) (1323.88)
p = 1.205 x 10⁻²⁷ kgm/s
(b)
wavelength of red light, λ = 440 nm
momentum of photon is given by;
velocity of electron is given by;
momentum of the electron is given by;
p = mv
p = (9.1 x 10⁻³¹) (1654.85)
p = 1.506 x 10⁻²⁷ kgm/s
(c) The momentum of the photon is equal to the momentum of the electron.