Answer: 2.94×10^8 J
Explanation:
Using the relation
T^2 = (4π^2/GMe) r^3
Where v= velocity
r = radius
T = period
Me = mass of earth= 6×10^24
G = gravitational constant= 6.67×10^-11
4π^2/GMe = 4π^2 / [(6.67x10^-11 x6.0x10^24)]
= 0.9865 x 10^-13
Therefore,
T^2 = (0.9865 × 10^-13) × r^3
r^3 = 1/(0.9865 × 10^-13) ×T^2
r^3 = (1.014 x 10^13) × T^2
To find r1 and r2
T1 = 120min = 120*60 = 7200s
T2 = 180min = 180*60= 10800s
Therefore,
r1 = [(1.014 x 10^13)7200^2]^(1/3) = 8.07 x 10^6 m
r2 = [(1.014 x 10^13)10800^2]^(1/3) = 10.57 x 10^6 m
Required Mechanical energy
= - GMem/2 [1/r2 - 1/r1]
= (6.67 x 10^-11 x 6.0 x 10^24 * 50)/2 * [(1/8.07 × 10^-6 )- (1/10.57 × 10^-6)]
= (2001 x 10^7)/2 * (0.1239 - 0.0945)
= (1000.5 × 10^7) × 0.0294
= 29.4147 × 10^7 J
= 2.94 x 10^8 J.
Answer:
at point F
Explanation:
To know the point in which the pendulum has the greatest potential energy you can assume that the zero reference of the gravitational energy (it is mandatory to define it) is at the bottom of the pendulum.
Then, when the pendulum reaches it maximum height in its motion the gravitational potential energy is
U = mgh
m: mass of the pendulum
g: gravitational constant
The greatest value is obtained when the pendulum reaches y=h
Furthermore, at this point the pendulum stops to come back in ts motion and then the speed is zero, and so, the kinetic energy (K=1/mv^2=0).
A) answer, at point F
<span>We can answer this using
the rotational version of the kinematic equations:</span><span>
θ = θ₀ + ω₀<span>t + ½αt²
-----> 1</span></span>
ω² = ω₀² + 2αθ
-----> 2
Where:
θ = final angular
displacement = 70.4 rad
θ₀ = initial
angular displacement = 0
ω₀ = initial angular
speed
ω = final angular speed
t = time = 3.80 s
α = angular acceleration
= -5.20 rad/s^2
Substituting the values
into equation 1:<span>
70.4 = 0 + ω₀(3.80)
+ ½(-5.20)(3.80)² </span><span>
ω₀ = (70.4
+ 37.544) / 3.80 </span><span>
ω₀ = 28.406
rad/s </span><span>
Using equation 2:
ω² = (28.406)² + 2(-5.2)70.4
ω = 8.65 rad/s
</span>
Given parameters;
Time taken to complete a lap = 8.667s
Radius of flower = 13.9cm
convert to SI unit of m, 100cm = 1m
13.9cm gives 
= 0.139m
Unknown = speed
To solve this problem, we need to first find the circumference of the flower.
Circumference of the circular flower = 2 π r
where r is the radius of the flower;
Circumference = 2 x 3.142 x 0.139 = 0.87m
Now to find the how fast the bug is travelling,
Speed = 
Since the bug covered 1 lap, the distance is 0.87m
Now input the parameters and solve for speed;
Speed = 
= 0.1m/s
The bug is travelling at a speed of 0.1m/s
Answer:
velocity = distance / time taken
= 200/4
= 50 m/s
is the correct answer
