 # Force, motion and energy problems and answers

Recent questions in Force, Motion and Energy anniferathonniz8km 2022-05-08

### The gravitational force between a planet and its moon is $6×{10}^{16}N$. 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 $6.29×{10}^{11}m$ away, showing it to be comparable to that of the father. The mass of Jupiter is about . 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

2022-05-06

### 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}_{traveled}={v}_{initial}.t+\frac{1}{2}a{t}^{2}$$a=\frac{2d}{{t}^{2}}$$a=\frac{2.1}{\left(.4003{\right)}^{2}}$$a=12.48\frac{m}{{s}^{2}}$2.${v}_{f}^{2}={v}_{i}^{2}+2ad$$a=\frac{{v}_{f}^{2}-{v}_{i}^{2}}{2d}$${v}_{f}=\frac{distance}{time}=\frac{1.0}{0.4003}=2.5\frac{m}{s}$$a=\frac{\left(2.5\frac{m}{s}{\right)}^{2}}{2.1m}$$a=3.125\frac{m}{{s}^{2}}$3.${v}_{f}={v}_{i}+at$$a=\frac{{v}_{f}-{v}_{i}}{t}$$a=\frac{2.5m/s-0}{0.4003s}$$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${\mathbf{F}}_{g}=\left({\mathbf{r}}_{j}-{\mathbf{r}}_{i}\right){m}_{j}{m}_{i}G/|{\mathbf{r}}_{j}-{\mathbf{r}}_{i}{|}^{3}$where ${\mathbf{r}}_{i}$ and ${\mathbf{r}}_{j}$ are the 3D position vectors of object $i$ and object $j$Is this right? If not, what is?Also, should$|{\mathbf{r}}_{j}-{\mathbf{r}}_{i}{|}^{3}$be the same as $\left[\left({x}_{j}-{x}_{i}{\right)}^{2}+\left({y}_{j}-{y}_{i}{\right)}^{2}+\left({z}_{j}-{z}_{i}{\right)}^{2}{\right]}^{3/2}$ or the vector $\left[|{x}_{j}-{x}_{i}|,|{y}_{j}-{y}_{i}|,|{z}_{j}-{z}_{i}|\right]$ 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 $100\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}\mathrm{m}$ per hour in $4.0\phantom{\rule{thinmathspace}{0ex}}\text{seconds}$. 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 ($0\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}\mathrm{p}\mathrm{h}$), final velocity ($100\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}\mathrm{p}\mathrm{h}$), and time ($4.0\phantom{\rule{thinmathspace}{0ex}}\mathrm{s}$).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 gravityCould 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: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 problemS = u²/2gBut g is variable with height as h approaches RSo dg = GM/(R+dr)² --- this is where I think I might be wrongHence dS = u²(R+dr)²/GMSo how do I go ahead? Carina Valenzuela 2022-04-12

### Gravitational pull vs. acceleration due to gravityIt 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 Logan Lamb 2022-04-07

### A satellite of the Earth has a mass of 100 kg and is at an altitude of (a) What is the gravitational potential energy of the satellite-Earth system?(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?(c) What force does the satellite exert on the Earth? Carol Valentine 2022-01-05

### A proton with an initial speed of 800,000 m/s is brought to rest by an electric field. a. Did the proton move into a region of higher potential or lower potential? b. What was the potential difference that stopped the proton? c. What was the initial kinetic energy of the proton, in electron volts? pogonofor9z 2022-01-03

### A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.240 m and the period is 3.08 s. a. What is the acceleration of the block when x = 0.160 m? socorraob 2022-01-02

### A 2.0 kg book is lying on a 0.75-m-high table. You pick it up and place it on a bookshelf 2.3 m above the floor. During this process, How much work does gravity do on the book? Lennie Davis 2021-12-22 Jean Blumer 2021-12-20