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Force, Motion and Energy

Recent questions in Force, Motion and Energy

Landon Mckinney 2022-05-08

The sun has a mass 333,000 times that of the earth. For a person on earth, the average distance to the center of the sun is 23,500 times the distance to the center of the earth. In magnitude, what is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?

Edith Mayer 2022-05-08

Why is $\frac{k}{4 π^{2}} = \frac{c}{M}$ and $f = (k m M) / r^{2}$ not $(4 π^{2}) / r^{2} \sqrt{M m c C}$ ?

Azzalictpdv 2022-05-08

Suppose the gravitational force between two planets is 6,097 N. If the first planet was 2 times more massive and the second planet was 9 times more massive, what would be the gravitational force between them?

Marissa Singh 2022-05-08

Acceleration due to gravity at Centre
Why is the acceleration due to gravity at the center of the earth $0$ ?
My Attempt
actually at the center distance from the surface is equal to the radius so the formula
$g^{'} = (1 - \frac{d}{R}) \times g$
yields $0$ .
But can anyone give me the other reason for this?

Azzalictpdv 2022-05-08

Acceleration due to gravity
Does acceleration due to gravity increase when an object at a said radius is doubled? Like for instance, if I said the radius of the earth is $5 k m$ (not to scale obviously) if I doubled that, so $10 k m$ will acceleration due to gravity double? Or maybe $g / 2$ ? Or would the acceleration stay the same no matter distance?

Aedan Tyler 2022-05-08

Acceleration due to gravitational force
I need some help with below. So according to Newton's 2nd law, $a = F / m$ , for a given mass, the acceleration depends on mass.
But acceleration due to gravity is independent of mass. There seems some contradiction; I am sure I am missing something, but I can't pin-point what that is.

anniferathonniz8km 2022-05-08

The gravitational force between a planet and its moon is $6 \times 10^{16} N$ . For another moon orbiting the same planet with twice the orbital radius and 3 times the mass, what is the gravitational force?

tuehanhyd8ml 2022-05-07

(a) Calculate the gravitational force exerted on a 3.00 kg baby by a 90 kg father 0.150 m away at birth (assisting so he is close).
(b) Calculate the force on the baby due to Jupiter if it is at its closest to the earth, some $6.29 \times 10^{11} m$ away, showing it to be comparable to that of the father. The mass of Jupiter is about $1.90 \times 10^{27} k g$ . Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

Ainsley Zimmerman 2022-05-07

An Earth satellite is in a circular orbit at an altitude of 500 km.Explain why the work done by the gravitational force actingon the satellite is zero. Using the work–energy theorem, whatcan you say about the speed of the satellite?

Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is 1 kilocalorie, which we define as 1 kcal = 4186 J. Metabolizing 1 gram of fat can release 9.00 kcal.

A student decides to try to lose weight by exercising. She plans to run up and down the stairs in a football stadium as fast as she can and as many times as necessary. Is this in itself a practical way to lose weight?

To evaluate the program, suppose she runs up a flight of 74 steps, each 0.173 m high, in 58.8 s. For simplicity, ignore the energy she uses in coming down (which is small). Assume that a typical efficiency for human muscles is 20.0%. This means that when your body converts 100 J from metabolizing fat, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into internal energy. Assume the student's mass is 52.8 kg.

How many times must she run the flight of stairs to lose 1 pound of fat? (1 lb = 0.454 kg)

What is her average power output, in watts and in horsepower, as she is running up the stairs? (1hp = 746 W)

ulcerat9jr 2022-05-02

Getting acceleration due to gravity from dropping ball experiment
This seems like pretty basic experiment, but I'm having a lot of trouble with it. Basically, I have two timer gates that measure time between two signals, and I drop metal ball between them. This way I'm getting distance traveled, and time. Ball is dropped from right above the first gate to make sure initial velocity is as small as possible (no way to make it 0 with this setup/timer). I'm assuming $v$ initial is $0 \frac{m}{s}$ . Gates are $1$ meter apart.
Times are pretty consistent, and average result from dropping ball from $1.0$ meters is $0.4003$ seconds.
So now I have $3$ [constant acceleration] equations that I can use to get $g$
1.
$d_{t r a v e l e d} = v_{i n i t i a l} . t + \frac{1}{2} a t^{2}$
$a = \frac{2 d}{t^{2}}$
$a = \frac{2.1}{(.4003)^{2}}$
$a = 12.48 \frac{m}{s^{2}}$
2.
$v_{f}^{2} = v_{i}^{2} + 2 a d$
$a = \frac{v_{f}^{2} - v_{i}^{2}}{2 d}$
$v_{f} = \frac{d i s t a n c e}{t i m e} = \frac{1.0}{0.4003} = 2.5 \frac{m}{s}$
$a = \frac{(2.5 \frac{m}{s})^{2}}{2.1 m}$
$a = 3.125 \frac{m}{s^{2}}$
3.
$v_{f} = v_{i} + a t$
$a = \frac{v_{f} - v_{i}}{t}$
$a = \frac{2.5 m / s - 0}{0.4003 s}$
$a = 6.25 \frac{m}{s^{2}}$
I'm getting three different results. And all of them are far from $9.8 \frac{m}{s^{2}}$ . No idea what I'm doing wrong.
Also, if I would drop that ball from different heights, and plot distance-time graph, how can I get acceleration from that?

Jordin Olsen 2022-05-02

Suppose the centre of mass of 2 bodies coincide , then how will we calculate the gravitational force between the 2 bodies ?

Araceli Soto 2022-04-30

How to calculate acceleration due to gravity in a 3D $N$ -Body system?
How do you calculate acceleration due to gravity for objects in 3D space?
My current understanding for the force due to gravity on object $i$ from object $j$ is
$F_{g} = (r_{j} - r_{i}) m_{j} m_{i} G / | r_{j} - r_{i} |^{3}$
where $r_{i}$ and $r_{j}$ are the 3D position vectors of object $i$ and object $j$
Is this right? If not, what is?
Also, should
$| r_{j} - r_{i} |^{3}$
be the same as $[(x_{j} - x_{i})^{2} + (y_{j} - y_{i})^{2} + (z_{j} - z_{i})^{2}]^{3 / 2}$ or the vector $[| x_{j} - x_{i} |, | y_{j} - y_{i} |, | z_{j} - z_{i} |]$ cubed?

Thaddeus Sanders 2022-04-12

What is the effect of acceleration due to gravity on horizontal acceleration?
The question is the following:
An object accelerates from rest to $100 k m$ per hour in $4.0 seconds$ . What fraction of the acceleration due to gravity is the car's acceleration?
From the question above, I can work out the acceleration (change in velocity over change in time) of the object using the given quantities: initial velocity ( $0 k p h$ ), final velocity ( $100 k p h$ ), and time ( $4.0 s$ ).
But what does gravitational acceleration have to do with this? Is the answer related to friction created by the downward acceleration due to gravity?

llunallenaipg5r 2022-04-12

Effects of spin on neutron star's surface acceleration due to gravity
Could a neutron star have sufficient mass and spin so that the centripetal force acts opposite to gravity to make the effective acceleration due to gravity zero or close to 1g? What would happen to the matter at the surface?

Cesar Mcguire 2022-04-12

Acceleration due to gravity: what's the derivation?
Modelling the Earth as a symmetric, spherical body (and by using the law of gravitation), we come up with the equation
$w = F_{g} = \frac{G m_{E} m}{R_{E}^{2}}$
How do we arrive to the equation to get the acceleration due to gravity at the earth's surface?
$g = \frac{G M_{E}}{R_{E}^{2}}$
Where:
$G = gravitational constant = 6.67 \times 10^{- 11} N$
$M_{E} = mass of Earth = 5.98 \times 10^{24} k g$
$R_{E} = Earth's radius = 6380 k m$
One thing I know of is the fact that we use Newton's second law, but how?

Jamir Melendez 2022-04-12

How to integrate acceleration due to gravity with height?
If I project a body at a very large velocity such that it reaches a height h which is comparable to Earth's radius, then how to derive an equation for 'h' in terms of initial velocity 'u' and other constants.
This is where I ended up with this problem
S = u²/2g
But g is variable with height as h approaches R
So dg = GM/(R+dr)² --- this is where I think I might be wrong
Hence dS = u²(R+dr)²/GM
So how do I go ahead?

Carina Valenzuela 2022-04-12

Gravitational pull vs. acceleration due to gravity
It might seem obvious but i can't imagine how is gravitational pull is different from acceleration due to gravity?

hard12bb30crg 2022-04-07

Why acceleration due to gravity is not reliably defined?
In Sean Carroll's Spacetime Geometry, there is the following line on Page No.50 in 2014th edition:
"The acceleration of a charged particle in an electromagnetic field is uniquely defined with respect to inertial frames.The EEP,on the other hand,implies that gravity is inescapable- there is no such thing as a "gravitationally neutral object" with respect to which we can measure the acceleration due to gravity. It follows that the acceleration due to gravity is not something that can be reliably defined,and therefore is of little use"
But, we do measure acceleration due to gravity of earth and moon. So why acceleration due to gravity is not reliably defined? Does this mean we cannot measure the true value of acceleration due to gravity of any massive object?

Brooklynn Hubbard 2022-04-07

A space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on it is 706 lb. What is the size of the force when it is at each of the following distances from Earth's center?
(a) 20,000 miles
(b) 30,000 miles
(c) 100,000 miles

When you have to provide correct answers to the questions based on motion equations physics, you must start with the examples that can help you learn more about the theory and see relevant examples. If you find it too challenging, start with the equations that help to determine the force of the motion as you estimate the energy that is being produced. It’s also helpful to compare several lab experiments to see the differences in how the concepts operate. Such an approach will help you to see the example of force and explain it both verbally and with the formulas.

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