Potential energy is the energy by virtue of object's height & kinetic energy by virtue of it's motion!
Hope this helps!
Answer:
U = 9.1 m/s
Explanation:
from the question we are given the following
time (t) = 1.8 s
angle = 23 degrees
acceleration due to gravity (g) = 9.8 m/s^{2}
let us first calculate the initial velocity (u) which too the first ball to its maximum height from the equation below
v = u + 0.5at
- The final velocity (v) is zero since the ball comes to rest
- The time (t) it takes to get to the maximum height would be half the time it is in the air, t = 0.5 x 1.8 = 0.9
therefore
0 = u - (0.5 x 9.8 x 0.9)
u = 7.9 m/s
for the second ball to get to the maximum height of the first ball, the vertical component of its initial velocity (U) must be the same as the initial velocity of the first ball. therefore
U sin 60 = 7.9
U = 7.9 ÷ sin 60
U = 9.1 m/s
Answer:
<em>Yes, work has been done on the mud.</em>
<em></em>
Explanation:
Work is done on a body, when a force is applied on the body to move it through a certain distance. In the case of the mud, the tire exerts a centripetal force on the mud. The centripetal force moves the mud along a path that follows the circle formed by the tire in one revolution of the tire. The total distance traveled is the circumference of the circle formed. <em>The work done on the mud is therefore the product of the centripetal force on the mud from the tire, and the circumference of the circle formed by the tire, usually expressed in radian.</em>
You have a point on a rectangular graph with coordinates (6, 8).
You want to describe the same location in polar coordinates ... R and Θ .
-- 'R' is the distance from the origin to the point.
-- 'Θ' is the angle you'd need to turn the x-axis counterclockwise
around the origin to make it pass through the point.
To change rectangular coordinates to polar coordinates:
R = √(x² + y²)
Θ = the angle whose tangent is (y / x) .
(6i + 8j) is the [Cartesian] vector that takes you from the origin to (6, 8) .
R = √(6² + 8²) = √(36 + 64) = √100 = 10
Θ = tan⁻¹ (8/6) = 53.13° (rounded)
In polar coordinates, the same point is 10 ∠53.13° .
Answer:
i. The radius 'r' of the electron's path is 4.23 ×
m.
ii. The frequency 'f' of the motion is 455.44 KHz.
Explanation:
The radius 'r' of the electron's path is called a gyroradius. Gyroradius is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field.
r = ![\frac{mv}{qB}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%7D%7BqB%7D)
Where: B is the strength magnetic field, q is the charge, v is its velocity and m is the mass of the particle.
From the question, B = 1.63 ×
T, v = 121 m/s, Θ =
(since it enters perpendicularly to the field), q = e = 1.6 ×
C and m = 9.11 ×
Kg.
Thus,
r =
÷ sinΘ
But, sinΘ = sin
= 1.
So that;
r = ![\frac{mv}{qB}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%7D%7BqB%7D)
= (9.11 ×
× 121) ÷ (1.6 ×
× 1.63 ×
)
= 1.10231 ×
÷ 2.608 × ![10^{-24}](https://tex.z-dn.net/?f=10%5E%7B-24%7D)
= 4.2266 ×
= 4.23 ×
m
The radius 'r' of the electron's path is 4.23 ×
m.
B. The frequency 'f' of the motion is called cyclotron frequency;
f = ![\frac{qB}{2\pi m}](https://tex.z-dn.net/?f=%5Cfrac%7BqB%7D%7B2%5Cpi%20m%7D)
= (1.6 ×
× 1.63 ×
) ÷ (2 ×
× 9.11 ×
)
= 2.608 ×
÷ 5.7263 × ![10^{-30}](https://tex.z-dn.net/?f=10%5E%7B-30%7D)
= 455442.4323
f = 455.44 KHz
The frequency 'f' of the motion is 455.44 KHz.