Answer
given,
mass of ball = 5.93 kg
length of the string = 2.35 m
revolve with velocity of 4.75 m/s
acceleration due to gravity = 9.81 m/s²
T cos θ = mg
T cos θ = 
T cos θ = 58.17






T² - 56.93T - 3383.75 = 0
T = 93.22 N

θ = 51.39°
Answer:
a) w = 7.27 * 10^-5 rad/s
b) v1 = 463.1 m/s
c) v1 = 440.433 m/s
Explanation:
Given:-
- The radius of the earth, R = 6.37 * 10 ^6 m
- The time period for 1 revolution T = 24 hrs
Find:
What is the earth's angular speed?
What is the speed of a point on the equator?
What is the speed of a point on the earth's surface located at 1/5 of the length of the arc between the equator and the pole, measured from equator?
Solution:
- The angular speed w of the earth can be related with the Time period T of the earth revolution by:
w = 2π / T
w = 2π / 24*3600
w = 7.27 * 10^-5 rad/s
- The speed of the point on the equator v1 can be determined from the linear and rotational motion kinematic relation.
v1 = R*w
v1 = (6.37 * 10 ^6)*(7.27 * 10^-5)
v1 = 463.1 m/s
- The angle θ subtended by a point on earth's surface 1/5 th between the equator and the pole wrt equator is.
π/2 ........... s
x ............ 1/5 s
x = π/2*5 = 18°
- The radius of the earth R' at point where θ = 18° from the equator is:
R' = R*cos(18)
R' = (6.37 * 10 ^6)*cos(18)
R' = 6058230.0088 m
- The speed of the point where θ = 18° from the equator v2 can be determined from the linear and rotational motion kinematic relation.
v2 = R'*w
v2 = (6058230.0088)*(7.27 * 10^-5)
v2 = 440.433 m/s
Answer:
<em>The work done by the car is 363 kJ</em>
Explanation:
Work : Work is said to be done when a Force moves an object through a certain distance. Work and Energy are interchangeable because they have the same unit. The unit of work is Joules (J).
Mathematically work done can be expressed as,
E = W = 1/2mv²
W = 1/2mv²................................ Equation 1
Where E = Energy, W = work done, m = mass of the car, v = velocity of the car
<em>Given: m=1500 kg, v=22 m/s</em>
<em>Substituting these values into equation 1</em>
<em>W = 1/2(1500)(22)²</em>
<em>W = 750 × 484</em>
<em>W = 363000 J</em>
<em>W = 363 kJ</em>
<em>Thus the work done by the car is 363 kJ</em>
Based on several theories made by scientists, planets are formed because of the accumulation of gases and other particles that are attracted to each other. These accumulated gases form into clumps and eventually the clumps get bigger and turn into a big orbital mass. The exoplanets may experience change over time through the observance of its orbit in a particular axis, and if there are other debris that might affect the planet's continuous growth.