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3 years ago

Why do we say that Neptune was the first planet to be discovered through the use of mathematics?

Physics

1 answer:

puteri [66]3 years ago

7 0

Answer:

explained

Explanation:

the Neptune was the first planet discovered through the use of mathematics by two astronomers one French and other English. This was breakthrough success in the field of astronomy that marked the importance of mathematics in astronomy. The discovery of the Neptune resulted from the need to explain the motion of Uranus, motion of which could not be explained by the gravitational effect of Jupiter and Neptune.It needed very complex mathematical equations to be Solved to explain it. The two astronomers were Joseph le Verrier and John Couch Adams.

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A tennis ball connected to a string is spun around in a vertical, circular path at a uniform speed. The ball has a mass m = 0.15

Oksanka [162]

1) 5.5 N

When the ball is at the bottom of the circle, the equation of the forces is the following:

$T-mg = m\frac{v^2}{R}$

where

T is the tension in the string, which points upward

mg is the weight of the string, which points downward, with

m = 0.158 kg being the mass of the ball

g = 9.8 m/s^2 being the acceleration due to gravity

$m \frac{v^2}{R}$ is the centripetal force, which points upward, with

v = 5.22 m/s being the speed of the ball

R = 1.1 m being the radius of the circular trajectory

Substituting numbers and re-arranging the formula, we find T:

$T=mg+m\frac{v^2}{R}=(0.158 kg)(9.8 m/s^2)+(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=5.5 N$

2) 3.9 N

When the ball is at the side of the circle, the only force acting along the centripetal direction is the tension in the string, therefore the equation of the forces becomes:

$T=m\frac{v^2}{R}$

And by substituting the numerical values, we find

$T=(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=3.9 N$

3) 2.3 N

When the ball is at the top of the circle, both the tension and the weight of the ball point downward, in the same direction of the centripetal force. Therefore, the equation of the force is

$T+mg=m\frac{v^2}{R}$

And substituting the numerical values and re-arranging it, we find

$T=m\frac{v^2}{R}-mg=(0.158 kg)\frac{5.22 m/s)^2}{1.1 m}-(0.158 kg)(9.8 m/s^2)=2.3 N$

4) 3.3 m/s

The minimum velocity for the ball to keep the circular motion occurs when the centripetal force is equal to the weight of the ball, and the tension in the string is zero; therefore:

$T=0\\mg = m\frac{v^2}{R}$

and re-arranging the equation, we find

$v=\sqrt{gR}=\sqrt{(9.8 m/s^2)(1.1 m)}=3.3 m/s$

7 0

3 years ago

What is the amount of work done when a force of 10N moves a 20kg mass of 8 meters?

Nataly_w [17]

Yo sup??

we should know that

work done=force*displacement

W=F.s

F=10 N

s=8 m

therefore

W=10*8

=80 N

Hope this helps.

3 0

3 years ago

A crate slides down a ramp that makes a 20∘ angle with the ground. to keep the crate from sliding too fast, paige pushes back on

shutvik [7]

The solution is:
Paige's force is (somewhat) against the direction of motion: Work = F * d Where F is the force; andd is the distance
Our f is 64 N and our distance is 20 and -3.6Plugging that in our equation will give us:
= 64N * cos20º * -3.6m = -217 J

8 0

3 years ago

Franny drew a diagram to compare images produced by concave and convex lenses.

yanalaym [24]

Answer:

virtual

Explanation:

4 0

3 years ago

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Cables and conductors installed on the side of a pole or building shall be protected up to ___feet above finished grade.

Allisa [31]

Answer:

10 feet.

Explanation:

Conductors are considered outside the building when they installed. The requirement of NEC is above 10 feet for the clearance after the final grade for service conductors and cables where they are connected with the building, above the sidewalks and the to other areas which are accessible to the pedestrians.

8 0

3 years ago