A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equa
l to the asteroid's radius and then falls straight down toward the surface of the asteroid. The acceleration of the ball at the top of its path is:_________
a. at its maximum value for the ball's flight.
b. equal to the acceleration at the surface of the asteroid.
c. equal to one-half the acceleration at the surface of the asteroid.
d. equal to one-fourth the acceleration at the surface of the asteroid.
a. at its maximum value for the ball's flight.
b. equal to the acceleration at the surface of the asteroid.
c. equal to one-half the acceleration at the surface of the asteroid.
d. equal to one-fourth the acceleration at the surface of the asteroid.
2 answers:
Answer:
(d) equal to one-fourth the acceleration at the surface of the asteroid.
Explanation:
From Newton's gravitational law, force between two objects (planet) is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
<u>Case 1</u>: when the ball rises to a height equal to the asteroid's radius
height, h = r
<u>Case 2:</u> when the ball rises to a height equal to the asteroid's radius and falls straight down toward the surface of the asteroid.
At top of its path, total height is 2r.
h = 2r
Therefore, the acceleration of the ball at the top of its path is equal to one-fourth the acceleration at the surface of the asteroid.
Option "d"
Answer:
d. equal to one-fourth the acceleration at the surface of the asteroid.
Explanation:
The explanation is attached as a picture with this answer
Newton's law of universal gravitation is being used to compare the accelerations at the surface and at the top of the ball's path.
as it can be seen in the explanation that the proportional form of the equation is used because we do not need to necessarily use to final form with "G" for comparison calculations.
As per the given scenario only difference between the two points in the gravitational field is the distance from center of the spherical asteroid, i.e. r.
It is taken 2r for the top is the path. hence we obtain (1/4)g as our answer.
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Answer:
a) 600 meters
b) between 0 and 10 seconds, and between 30 and 40 seconds.
c) the average of the magnitude of the velocity function is 15 m/s
Explanation:
a) In order to find the magnitude of the car's displacement in 40 seconds,we need to find the area under the curve (integral of the depicted velocity function) between 0 and 40 seconds. Since the area is that of a trapezoid, we can calculate it directly from geometry:
b) The car is accelerating when the velocity is changing, so we see that the velocity is changing (increasing) between 0 and 10 seconds, and we also see the velocity decreasing between 30 and 40 seconds.
Notice that between 10 and 30 seconds the velocity is constant (doesn't change) of magnitude 20 m/s, so in this section of the trip there is NO acceleration.
c) To calculate the average of a function that is changing over time, we do it through calculus, using the formula for average of a function:
Notice that the limits of integration for our case are 0 and 40 seconds, and that we have already calculated the area under the velocity function (the integral) in step a), so the average velocity becomes:
Answer:
Therefore the ratio of diameter of the copper to that of the tungsten is
Explanation:
Resistance: Resistance is defined to the ratio of voltage to the electricity.
The resistance of a wire is
- directly proportional to its length i.e
- inversely proportional to its cross section area i.e
Therefore
ρ is the resistivity.
The unit of resistance is ohm (Ω).
The resistivity of copper(ρ₁) is 1.68×10⁻⁸ ohm-m
The resistivity of tungsten(ρ₂) is 5.6×10⁻⁸ ohm-m
For copper:
......(1)
Again for tungsten:
........(2)
Given that and
Dividing the equation (1) and (2)
[since
and
]
Therefore the ratio of diameter of the copper to that of the tungsten is