1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vesna [10]
3 years ago
7

A projectile of mass m is fired straight upward from the surface of an airless planet of radius R and mass M with an initial spe

ed equal to the escape speed vesc (meaning the projectile will just barely escape the planet's gravity -- it will asymptotically approach infinite distance and zero speed.) What is the correct expression for the projectile's kinetic energy when it is a distance 9R from the planet's center (8R from the surface). Ignore the gravity of the Sun and other astronomical bodies. KE (at r = 9R) is:a. GMm/9Rb. GMm/8Rc. 1/2mvesc^2d. -GMm/8Re. None of these
Physics
1 answer:
motikmotik3 years ago
6 0

Answer:

K = G Mm / 9R

Explanation:

Expression for escape velocity V_e = \sqrt{\frac{2GM}{R} }

Kinetic energy at the surface = 1/2 m V_e ²

= 1/2 x m x 2GM/R

GMm/R

Potential energy at the surface

= - GMm/R

Total energy = 0

At height 9R ( 8R from the surface )

potential energy

= - G Mm / 9R

Kinetic energy = K

Total energy will be zero according to law of conservation of mechanical energy

so

K  - G Mm / 9R = 0

K = G Mm / 9R

You might be interested in
Cooling down after a workout allows the oxygen to continuing moving through the body and keeps the muscles from tightening up to
Liono4ka [1.6K]

Answer: true

Explanation:

7 0
3 years ago
Read 2 more answers
The force a magnet exerts on another magnet, on iron or a similar metal, or on moving charges is
In-s [12.5K]
The answer is a magnetic force.
7 0
3 years ago
Read 2 more answers
A 2-kg bowling ball sits on top of a building that is 40 meters tall.
Dahasolnce [82]
The bowling ball is at rest, so it only has gravitational potential energy.

Ug = mgy
Ug = (2)(9.8)(40) = 784 J

Need any more help?
6 0
3 years ago
Read 2 more answers
Which seismic waves are generally the last to arrive after an earthquake?
34kurt
You're answer is B. P waves are more dynamic and have a great autonomy to be able generate a earthquake.
5 0
3 years ago
A thin spherical spherical shell of radius R which carried a uniform surface charge density σ. Write an expression for the volum
ozzi

Answer:

Explanation:

From the given information:

We know that the thin spherical shell is on a uniform surface which implies that both the inside and outside the charge of the sphere are equal, Then

The volume charge distribution relates to the radial direction at r = R

∴

\rho (r) \  \alpha  \  \delta (r -R)

\rho (r) = k \  \delta (r -R) \ \  at \ \  (r = R)

\rho (r) = 0\ \ since \ r< R  \ \ or  \ \ r>R---- (1)

To find the constant k, we  examine the total charge Q which is:

Q = \int \rho (r) \ dV = \int \sigma \times dA

Q = \int \rho (r) \ dV = \sigma \times4 \pi R^2

∴

\int ^{2 \pi}_{0} \int ^{\pi}_{0} \int ^{R}_{0} \rho (r) r^2sin \theta  \ dr \ d\theta \ d\phi = \sigma \times 4 \pi R^2

\int^{2 \pi}_{0} d \phi* \int ^{\pi}_{0} \ sin \theta d \theta * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2

(2 \pi)(2) * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2

Thus;

k * 4 \pi  \int ^{R}_{0}  \delta (r -R) * r^2dr = \sigma \times  R^2

k * \int ^{R}_{0}  \delta (r -R)  r^2dr = \sigma \times  R^2

k * R^2= \sigma \times  R^2

k  =   R^2 --- (2)

Hence, from equation (1), if k = \sigma

\mathbf{\rho (r) = \delta* \delta (r -R)  \ \  at   \ \  (r=R)}

\mathbf{\rho (r) =0 \ \  at   \ \  rR}

To verify the units:

\mathbf{\rho (r) =\sigma \ *  \ \delta (r-R)}

↓         ↓            ↓

c/m³    c/m³  ×   1/m            

Thus, the units are verified.

The integrated charge Q

Q = \int \rho (r) \ dV \\ \\ Q = \int ^{2 \ \pi}_{0} \int ^{\pi}_{0} \int ^R_0 \rho (r) \ \ r^2 \ \  sin \theta  \ dr \ d\theta \  d \phi  \\ \\  Q = \int ^{2 \pi}_{0} \  d \phi  \int ^{\pi}_{0} \ sin \theta  \int ^R_{0} \rho (r) r^2 \ dr

Q = (2 \pi) (2) \int ^R_0 \sigma * \delta (r-R) r^2 \ dr

Q = 4 \pi  \sigma  \int ^R_0  * \delta (r-R) r^2 \ dr

Q = 4 \pi  \sigma  *R^2    since  ( \int ^{xo}_{0} (x -x_o) f(x) \ dx = f(x_o) )

\mathbf{Q = 4 \pi R^2  \sigma  }

6 0
3 years ago
Other questions:
  • An ideal spring is mounted horizontally, with its left end fixed. The force constant of the spring is 170 N/m. A glider of mass
    8·1 answer
  • Calculate the acceleration of a skier heading down a 10.0º slope, assuming the coefficient of friction for waxed wood on wet sno
    15·1 answer
  • What is the marble's range if it is fired horizontally from 1.6 m above the ground?
    9·1 answer
  • Rihanna can go from 0-60 miles per hour in 3.5 seconds. Calculate the acceleration.
    11·1 answer
  • Are 50% of psychologists clinicians?
    8·1 answer
  • Which equation represents the total energy of a system
    6·1 answer
  • What is the difference between diatomic and poly-atomic molecules? Site some examples.
    8·1 answer
  • What color do blind people see lol
    14·2 answers
  • Explain the benefits of understanding sound waves properties in real life.
    11·1 answer
  • A skateboarder, starting from the top of a ramp 4,5 m above the ground, skates down the ramp. The mass of the skateboarder and h
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!