Answer:
Incomplete question. Complete question is: An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is twice the magnitude of the tangential acceleration. Determine the angle through which the drill rotates by this point.
The answer is : Δ θ = 1 rad
Explanation:
Ok, so the condition involves the centripetal acceleration and the tangential acceleration, so let’s start by writing expressions for each:
Ac= centripetal acceleration At= tangential acceleration
Ac = V² / r At = r α
Because we have to determine the angle ultimately, therefore we should convert the linear velocity into angular velocity in the expression for centripetal acceleration
V = r ω
Ac = (r ω)² / r = r² ω² / r
Ac = r ω²
now that we have expressions for the centripetal and tangential acceleration, we can write an equation that expresses the condition given: The magnitude of the centripetal acceleration is twice the magnitude of the tangential acceleration.
Ac = 2 At
That is,
r ω² = 2 r α
it is equivalent to;
ω² = 2 α
now we have the relation between angular speed and angular acceleration, but we also need to determine the angular displacement as well. Therefore choose a kinematics equation that doesn’t involve time because time is not mentioned in the question. Thus,
ω² – ω°² = 2 α Δ θ
such that ω° = 0
and ω² = 2 α
therefore;
2 α - 0 = 2 α Δ θ
2 α = 2 α Δ θ
So the angle will be : Δ θ = 1 rad
The kinetic energy (KE) of a 0.155 kg arrow that is shot from ground level, upward at 31.4 m/s, when it is 30.0 m above the ground is 30.85 J
Assuming air friction is negligible,
a = - 9.8 m / s²
u = 31.4 m / s
s = 30 m
v² = u² + 2 a s
v² = 31.4² + ( 2 * - 9.8 * 30 )
v² = 985.96 - 588
v² = 397.96 m / s
KE = 1 / 2 m v²
KE = 1 / 2 * 0.155 * 397.96
KE = 0.0775 * 397.96
KE = 30.85 J
Therefore, the kinetic energy ( KE ) when it is 30.0 m above the ground is 30.85 J
To know more about kinetic energy
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It's Endorphins. That's a pain killer produced by the brain.
Answer:
Its position after 4 seconds is 62 meters.
Explanation:
It is given that,
The acceleration of the particle is given by equation :

Also, 



At t = 0,
. So, c = 3

Also,
, s is the position



At t = 0,
. So, c' = 10

At t = 4 s

s = 62 m
So, at t = 4 seconds the position of the particle is 62 meters. Hence, this is the required solution.
A boy shooting a rubber band across the classroom -->
Elastic potential energy transformed into kinetic energy
<span>The initial energy is the energy stored in the muscles of the boy's arm, which is elastic potential energy. This is converted into motion of the rubber, therefore kinetic energy
A child going down a slide on a playground --> </span>Gravitational potential energy transformed into kinetic energy
On top of the slide, all the energy of the child is gravitational potential energy due to its height with respect to the ground (E=mgh). when it moves down the slide, this is converted into kinetic energy, because the child acquires a speed v (E=1/2 mv^2)
<span>
Rubbing your hands together to warm them on a cold day --> </span>Kinetic energy being transformed into thermal energy <span>
When rubbing hands, we are moving them (kinetic energy), and this energy raises the temperature of the hand's surface (thermal energy)
Turning on a battery operated light --> </span>
Chemical potential energy transformed into radiant energy <span>
A battery works by mean of chemical reactions (chemical potential energy), producing light (so, emitting energy by radiation, i.e. radiant energy)
Using a dc electric motor --> </span> Electrical energy transformed into kinetic energy<span>
A dc electric motor works using currents (so, electrical energy), and the energy produced can be used for example to accelerate a car (kinetic energy)
Using a gas power heater to warm a room --> </span>Chemical potential energy transformed into thermal energy
<span>A gas power heater burns gases (so, chemical reaction, i.e. chemical potential energy) to raise the temperature of the room (thermal energy)
Using a hand crank generator to produce electric current --> Kinetic energy transformed into electrical energy
In a hand-crank generator, the handle is being rotated (kinetic energy) in order to produce an electric current (electrical energy)
Using the light in your room that is plugged into the wall --> </span>Electrical energy transformed into radiant energy
<span>The lamp works by using electrical current flowing into a resistor (electrical energy) and it produces light, so it emits energy by electromagnetic radiation (radiant energy)
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