Complete Question:
A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns.
They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/s2 ) i + (4.00 m/s2 ) j .At that instant and in unit-vector notation, what is the acceleration of the wallet
Answer:
aw = 3 i + 6 j m/s2
Explanation:
- Since both objects travel in uniform circular motion, the only acceleration that they suffer is the centripetal one, that keeps them rotating.
- It can be showed that the centripetal acceleration is directly proportional to the square of the angular velocity, as follows:
- Since both objects are located on the same radial line, and they travel in uniform circular motion, by definition of angular velocity, both have the same angular velocity ω.
∴ ωp = ωw (2)
⇒
- Dividing (4) by (3), from (2), we have:
Answer:
The distance is 300 m.
Explanation:
Given that,
Time = 30 s
Speed = 80 m/s
Distance = 1200 m
Speed of smaller plane = 40 m/s
We need to calculate the acceleration
Using equation of motion
Put the value in the equation
We need to calculate the distance
Using equation of motion
Put the value in the equation
Hence, The distance is 300 m.
Answer:
<em>The second particle will move through the field with a radius greater that the radius of the first particle</em>
Explanation:
For a charged particle, the force on the particle is given as
also recall that work is force times the distance traveled
work = F x d
so, the work on the particle = F x d,
where the distance traveled by the particle in one revolution =
Work on a particle = 2πrF =
This work is proportional to the energy of the particle.
And the work is also proportional to the radius of travel of the particles.
Since the second particle has a bigger speed v, when compared to the speed of the first particle, then, the the second particle has more energy, and thus will move through the field with a radius greater that the radius of the first particle.
Answer:
(a) 0.17 m
(b) 5.003 m
(c) 6.38 × N
(d) 7.37 × N
Explanation:
(a) The minimum value of will occur when q3 = 0 m or at origin and q1, q2 are at 0.17 m so the distance between q3 and q1, q2 is 0.17 m, therefore the <em>minimum value of x= 0.17 m</em>.
(b) The maximum value of x will occur when q3 = 5 m because it is said in the question that 5 is the maximum distance travelled by q3. To find the hypotenuse i.e. the distance between q3 and q1,q2, we use Pythagoras theorem.
<em>Hence, the maximum distance is 5.002 m</em>
(c) For minimum magnitude we use the minimum distance calculated in (a)
Minimum Distance = 0.17 m
For electrostatic force=
×
(d) For maximum magnitude, we use the maximum distance calculated in (b)
Maximum Distance = 5.002 m
Using the formula for electrostatic force again:
F =
F= 7.37× N