The orbital period increases if the orbital distance is increased.
The normal force of the force given is calculated through the equation,
Fn = F(sin θ)
where Fn is the normal force, F is the force, and θ is the angle.
Fn = (25 N)(sin 60°) = 21.65 N
The x-component of the force applied is,
Fx = (25 N)(cos 60°) = 12.5 N
The value of the coefficient of static friction is calculated through the equation,
F = μFn
μ = Fx / Fn = 12.5 N / 21.65 N = 0.577
A couple of things, if the shuttle burned all of it's fuel before entering Earth's atmosphere then that means that the shuttle was accelerating towards Earth until it ran out of fuel. At that point, there is little to no air resistance (friction) by the lack of an atmosphere so it keeps accelerating due to Earth's gravitational force. The closer the shuttle gets to Earth the stronger the gravitational pull the shuttle experiences. Note that, once the shuttle reaches Earth's atmosphere it will cause significant amount of friction and thus will cause the shuttle to slow down.
- The length of the cross product of two vectors
- The scalar triple product of the vectors a, b, and c
- The volume of the parallelepiped determined by the vectors a, b, and c is the magnitude of their scalar triple product.
<u>Explanation</u>:
- The length of the cross product of two vectors is
| a
b | = |a| |b| sin θ
- The length of the cross product of two vectors is equal to the area of the parallelogram determined by the two vectors (see figure below).
| a
b | = - | b
a |
- Multiplication by scalars:
(ca)
b = c (a
b) = a
(cb)
a
(b + c) = (a
b) + (a
c)
- The scalar triple product of the vectors a, b, and c:
a . (b
c) = (a
b) . c
- The magnitude of the scalar triple product is the volume of the parallelepiped of the vectors a, b, and c.
- The vector triple product of the vectors a, b, and c is given as
a
(b
c) = (a.c) b - (a.b)
c
Answer:
5.33 cm
Explanation:
The lens equation states that:

where
f is the focal length
p is the distance of the object from the lens
q is the distance of the image from the lens
In this problem,
p = 8 cm
q = 16 cm ( the sign is positive since the image is real, which means it is formed on the other side of the lens)
Substituting into the equation,

