A 1.5 kg object is located at a distance of 1.7 x10^{6} m from the center of a larger object whose mass is 7.4 x 10^{22} kg.

- (a) What is the magnitude of the force acting on the smaller object?
*(3 points)* - (b) What is the magnitude of the force acting on the larger object?
*(3 points)* - (c) What is the acceleration of the smaller object when it is released?
*(3 points)*

- 2.56 N
- 2.56 N
- 1.71 m/s
^{2}

Step | Formula Derivation | Reasoning |
---|---|---|

1 | F = G \frac{m_1 m_2}{r^2} | Newton’s law of universal gravitation, where F is the gravitational force, G is the gravitational constant, m_1 and m_2 are the masses, and r is the distance between the centers of the two objects. |

**2. Magnitude of the Force Acting on the Larger Object**

Step | Explanation |
---|---|

1 | The magnitude of the force on the larger object is equal to the magnitude of the force on the smaller object (Newton’s Third Law). |

**3. Acceleration of the Smaller Object**

Step | Formula Derivation | Reasoning |
---|---|---|

1 | a = \frac{F}{m_1} | Acceleration of the smaller object, where F is the gravitational force and m_1 is its mass. |

Let’s perform the calculations using these steps.

- Magnitude of the force acting on the smaller object: \boxed{2.56, \text{N}}
- Magnitude of the force acting on the larger object: \boxed{2.56, \text{N}} (equal in magnitude to the force on the smaller object)
- Acceleration of the smaller object when it is released: \boxed{1.71, \text{m/s}^2}

Phy can also check your working. Just snap a picture!

- Statistics

Intermediate

Proportional Analysis

GQ

The Earth’s radius is 6.37 x 10^{6} m. What is the radius of a planet that has the same mass as earth but on which the free-fall acceleration is 5.50 m/s^{2}？

- Gravitation

Intermediate

Proportional Analysis

GQ

A child on Earth has a weight of 500N. Determine the weight of the child if the earth was to triple in both mass and radius (3M and 3r).

- Gravitation, Linear Forces

Intermediate

Proportional Analysis

MCQ

The exoplanet HD 69830b has a mass 10 times that of the Earth and a radius 5 times that of the Earth. The value of *g* on HD 69830b is most nearly

- Gravitation

Intermediate

Mathematical

FRQ

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a 50 km diameter circular orbit with a period of 11 days.

- Circular Motion, Gravitation

Intermediate

Proportional Analysis

FRQ

Imagine a hypothetical planet that has two moons. Moon #1 is in a circular orbit of radius R and has a mass M.

- Gravitation

Advanced

Conceptual

MCQ

While traveling in its elliptical orbit around the Sun, Mars gains speed during the part of the orbit where it is getting closer to the Sun. Which of the following can be used to explain this gain in speed?

- Angular Momentum, Energy, Gravitation, Rotational Motion, Torque

Advanced

Mathematical

GQ

Find the net gravitational force on a 2.0 kg sphere midway between a 4.0 kg sphere and a 7.0 kg sphere that are 1.2 m apart.

- Gravitation

Advanced

Mathematical

GQ

A spacecraft somewhere in between the earth and the moon experiences 0 net force acting on it. This is because the earth and the moon pull the spacecraft in equal but opposite directions. Find the distance *D* away from Earth, such that the spacecraft experiences zero net force. The distance between the Moon and Earth is ~3.844 x 10^{8} m.

NOTE: You may need the mass of the earth and moon. You can find this in the formula table.

- Gravitation, Linear Forces

Intermediate

Mathematical

GQ

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the radius of a geosynchronous orbit about the neutron star? The mass of the sun can be found in the formula sheet above.

- Circular Motion, Gravitation

Advanced

Proportional Analysis

MCQ

*v _{A}* . Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?

- Circular Motion, Gravitation

- 2.56 N
- 2.56 N
- 1.71 m/s
^{2}

By continuing you (1) agree to our Terms of Sale and Terms of Use and (2) consent to sharing your IP and browser information used by this site’s security protocols as outlined in our Privacy Policy.

Kinematics | Forces |
---|---|

\Delta x = v_i t + \frac{1}{2} at^2 | F = ma |

v = v_i + at | F_g = \frac{G m_1m_2}{r^2} |

a = \frac{\Delta v}{\Delta t} | f = \mu N |

R = \frac{v_i^2 \sin(2\theta)}{g} |

Circular Motion | Energy |
---|---|

F_c = \frac{mv^2}{r} | KE = \frac{1}{2} mv^2 |

a_c = \frac{v^2}{r} | PE = mgh |

KE_i + PE_i = KE_f + PE_f |

Momentum | Torque and Rotations |
---|---|

p = m v | \tau = r \cdot F \cdot \sin(\theta) |

J = \Delta p | I = \sum mr^2 |

p_i = p_f | L = I \cdot \omega |

Simple Harmonic Motion |
---|

F = -k x |

T = 2\pi \sqrt{\frac{l}{g}} |

T = 2\pi \sqrt{\frac{m}{k}} |

Constant | Description |
---|---|

g | Acceleration due to gravity, typically 9.8 , \text{m/s}^2 on Earth’s surface |

G | Universal Gravitational Constant, 6.674 \times 10^{-11} , \text{N} \cdot \text{m}^2/\text{kg}^2 |

\mu_k and \mu_s | Coefficients of kinetic (\mu_k) and static (\mu_s) friction, dimensionless. Static friction (\mu_s) is usually greater than kinetic friction (\mu_k) as it resists the start of motion. |

k | Spring constant, in \text{N/m} |

M_E = 5.972 \times 10^{24} , \text{kg} | Mass of the Earth |

M_M = 7.348 \times 10^{22} , \text{kg} | Mass of the Moon |

M_M = 1.989 \times 10^{30} , \text{kg} | Mass of the Sun |

Variable | SI Unit |
---|---|

s (Displacement) | \text{meters (m)} |

v (Velocity) | \text{meters per second (m/s)} |

a (Acceleration) | \text{meters per second squared (m/s}^2\text{)} |

t (Time) | \text{seconds (s)} |

m (Mass) | \text{kilograms (kg)} |

Variable | Derived SI Unit |
---|---|

F (Force) | \text{newtons (N)} |

E, PE, KE (Energy, Potential Energy, Kinetic Energy) | \text{joules (J)} |

P (Power) | \text{watts (W)} |

p (Momentum) | \text{kilogram meters per second (kgm/s)} |

\omega (Angular Velocity) | \text{radians per second (rad/s)} |

\tau (Torque) | \text{newton meters (Nm)} |

I (Moment of Inertia) | \text{kilogram meter squared (kgm}^2\text{)} |

f (Frequency) | \text{hertz (Hz)} |

General Metric Conversion Chart

Conversion Example

Example of using unit analysis: Convert 5 kilometers to millimeters.

Start with the given measurement:

`\text{5 km}`

Use the conversion factors for kilometers to meters and meters to millimeters:

`\text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}}`

Perform the multiplication:

`\text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}} = 5 \times 10^3 \times 10^3 \, \text{mm}`

Simplify to get the final answer:

`\boxed{5 \times 10^6 \, \text{mm}}`

Prefix | Symbol | Power of Ten | Equivalent |
---|---|---|---|

Pico- | p | 10^{-12} | 0.000000000001 |

Nano- | n | 10^{-9} | 0.000000001 |

Micro- | µ | 10^{-6} | 0.000001 |

Milli- | m | 10^{-3} | 0.001 |

Centi- | c | 10^{-2} | 0.01 |

Deci- | d | 10^{-1} | 0.1 |

(Base unit) | – | 10^{0} | 1 |

Deca- or Deka- | da | 10^{1} | 10 |

Hecto- | h | 10^{2} | 100 |

Kilo- | k | 10^{3} | 1,000 |

Mega- | M | 10^{6} | 1,000,000 |

Giga- | G | 10^{9} | 1,000,000,000 |

Tera- | T | 10^{12} | 1,000,000,000,000 |

- Some answers may be slightly off by 1% depending on rounding, etc.
- Answers will use different values of gravity. Some answers use 9.81 m/s
^{2}, and other 10 m/s^{2 }for calculations. - Variables are sometimes written differently from class to class. For example, sometime initial velocity v_i is written as u ; sometimes \Delta x is written as s .
- Bookmark questions that you can’t solve so you can come back to them later.
- Always get help if you can’t figure out a problem. The sooner you can get it cleared up the better chances of you not getting it wrong on a test!

The most advanced version of Phy. Currently 50% off, for early supporters.

per month

Billed Monthly. Cancel Anytime.

Trial –> Phy Pro

- Unlimited Messages
- Unlimited Image Uploads
- Unlimited Smart Actions
- 30 --> 300 Word Input
- 3 --> 15 MB Image Size Limit
- 1 --> 3 Images per Message
- 200% Memory Boost
- 150% Better than GPT
- 75% More Accurate, 50% Faster
- Mobile Snaps
- Focus Mode
- No Ads