The linear speed of the ladybug is 4.1 m/s
Explanation:
First of all, we need to find the angular speed of the lady bug. This is given by:
where
T is the period of revolution
The period of revolution is the time taken by the ladybug to complete one revolution: in this case, since it does 1 revolution every second, the period is 1 second:
T = 1 s
Therefore, the angular speed is
Now we can find the linear speed of the ladybug, which is given by
where:
is the angular speed
r = 65.0 cm = 0.65 m is the distance of the ladybug from the axis of rotation
Substituting, we find
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Answer: A- It would increase
Explanation:
According to the law of universal gravitation:
Where:
is the module of the attraction force exerted between both objects
is the universal gravitation constant.
and 
are the masses of both objects
is the distance between both objects
As we can see, the gravity force is directly proportional to the mass of the bodies or objects and inversely proportional to the square of the distance that separates them.
In other words:
<h2>If we decrease the distance between both objects, the gravitational force between them will increase. </h2>
The final velocity is 5.87 m/s
<u>Explanation:</u>
Given-
mass, = 72 kg
speed, 
= 5.8 m/s
, = 45 kg
,
= 12 m/s
Θ = 60°
Final velocity, v = ?
Applying the conservation of momentum:
X + X = ( + ) v
72 X 5.8 + 45 X 12 X cos 60° = (72 + 45) v
v = 417.6 + 540 X 
v = 417.6 + 
v = 5.87 m/s
The final velocity is 5.87 m/s
Answer:
A: The acceleration is 7.7 m/s up the inclined plane.
B: It will take the block 0.36 seconds to move 0.5 meters up along the inclined plane
Explanation:
Let us work with variables and set
As shown in the attached free body diagram, we choose our coordinates such that the x-axis is parallel to the inclined plane and the y-axis is perpendicular. We do this because it greatly simplifies our calculations.
Part A:
From the free body diagram we see that the total force along the x-axis is:
Now the force of friction is 
where 
is the normal force and from the diagram it is 
Thus 
Therefore,
Substituting the value for 
we get:
Now acceleration is simply
The negative sign indicates that the acceleration is directed up the incline.
Part B:
Which can be rearranged to solve for t:
Substitute the value of 
and 
and we get:
which is our answer.
Notice that in using the formula to calculate time we used the positive value of 
, because for this formula absolute value is needed.
Answer: v = 880m/s
Explanation: The length of a string is related to the wavelength of sound passing through the string at the fundamental frequency is given as
L = λ/2 where L = length of string and λ = wavelength.
But L = 1m
1 = λ/2
λ = 2m.
But the frequency at fundamental is 440Hz and
V = fλ
Hence
v = 440 * 2
v = 880m/s
