Answer:
hmax = 1/2 · v²/g
Explanation:
Hi there!
Due to the conservation of energy and since there is no dissipative force (like friction) all the kinetic energy (KE) of the ball has to be converted into gravitational potential energy (PE) when the ball comes to stop.
KE = PE
Where KE is the initial kinetic energy and PE is the final potential energy.
The kinetic energy of the ball is calculated as follows:
KE = 1/2 · m · v²
Where:
m = mass of the ball
v = velocity.
The potential energy is calculated as follows:
PE = m · g · h
Where:
m = mass of the ball.
g = acceleration due to gravity (known value: 9.81 m/s²).
h = height.
At the maximum height, the potential energy is equal to the initial kinetic energy because the energy is conserved, i.e, all the kinetic energy was converted into potential energy (there was no energy dissipation as heat because there was no friction). Then:
PE = KE
m · g · hmax = 1/2 · m · v²
Solving for hmax:
hmax = 1/2 · v² / g
The wave diagramed in blue.
<span>(1) </span>Through the Second
Law of motion, the equation for Force is:
F = m x a
Where
m is mass and a is acceleration (deceleration)
<span>(2) </span>Distance is
calculated through the equation,
D
= Vi^2 / 2a
Where
Vi is initial velocity
<span>(3) </span>Work is calculated
through the equation,
W = F x D
Substituting
the known values,
Part
A:
<span>(1) </span> F = (85
kg)(2 m/s^2) = 170 N
<span>(2) </span> D = (37
m/s)^2 / (2)(2 m/s^2) = 9.25 m
<span>(3) </span> W = (170
N)(9.25 m) = 1572.5 J
Part
B:
<span>(1) </span> F = (85 kg)(4
m/s^2) = 340 N
<span>(2) </span>D = (37 m/s)^2 /
(2)(4 m/s^2) = 4.625 m
<span>(3) </span><span> W = (340
N)(4.625 m) = 1572.5 J</span>
<h3>Option B</h3><h3>The time constant of a 10 H inductor and a 200 ohm resistor connected in series is 50 millisecond</h3>
<em><u>Solution:</u></em>
Given that,
10 H inductor and a 200 ohm resistor connected in series
To find: time constant
<em><u>The time constant in seconds is given as:</u></em>
Where,
L is the inductance in henry and R is the resistance in ohms
Convert to millisecond
1 second = 1000 millisecond
0.05 second = 0.05 x 1000 = 50 millisecond
Thus time constant is 50 millisecond
