{"id":9459,"date":"2026-06-01T21:33:48","date_gmt":"2026-06-01T21:33:48","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=9459"},"modified":"2026-06-01T21:33:48","modified_gmt":"2026-06-01T21:33:48","slug":"gravitational-field-and-contact-forces","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/gravitational-field-and-contact-forces\/","title":{"rendered":"Gravitational Field And Contact Forces"},"content":{"rendered":"

Unit: <\/strong>Dynamics<\/strong><\/h2>\n

Chapter: <\/strong>Gravitational Field and Contact Forces<\/strong><\/h3>\n

Reference: AP Physics Algebra, <\/em>Dynamics, Gravitational Field and Contact Forces, Gravitational Field, Gravitational field strength, Gravitational Force between Point Masses, Gravitational Potential and Potential energy, Contact forces, Frictional Force, Laws of Static Friction, Angle of Friction, The angle of Response<\/p>\n

After studying this chapter, you should be able to:<\/strong><\/p>\n

    \n
  • state the law of gravitation;<\/li>\n
  • analyse the variation in the value of the acceleration due to gravity with height, depth and latitude;<\/li>\n
  • distinguish between gravitational potential and gravitational potential energy;<\/li>\n
  • state the contact force.<\/li>\n<\/ul>\n

    Gravitational Field<\/h3>\n

    A force field is an area in which an object experiences a non-contact force.<\/p>\n

    Force fields <\/strong>are formed during the interaction of masses, static charges or moving charges. Different types of fields are formed depending on which interaction takes place:<\/p>\n

    Gravitational fields <\/strong>– formed during the interaction of masses<\/p>\n

    Electric fields <\/strong>– formed during the interaction of charges.<\/p>\n

    Therefore, a gravitational field is an area where objects with mass experience a non-contact force.<\/p>\n

    There are two types of gravitational fields:<\/p>\n

    Uniform field – <\/strong>Exerts the same gravitational force on a mass everywhere in the field<\/p>\n

    Radial field – <\/strong>The force exerted depends on the position of the object in the field<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

     <\/p>\n

     <\/p>\n

    The arrows on the field lines show the direction that a force acts on a mass, and the distance between field lines represents the strength of the force exerted by the field in that region. The closer the lines, the stronger the gravitational field strength.<\/p>\n

    The Earth’s gravitational field is radial, however very close to the surface it is almost completely uniform.<\/p>\n

    Gravitational field strength (g): <\/strong><\/p>\n

    Gravitational field strength is the force per unit mass exerted by a gravitational field on an object. This value is constant in a uniform field, but varies in a radial field. You can use the following formula to calculate the gravitational field strength:<\/p>\n

                                               G=F\/m<\/em><\/p>\n

    Where F is the force exerted and m is the mass of the object in the field.<\/p>\n

    Gravitational Force between Point Masses<\/h3>\n

     <\/p>\n

    Gravity <\/strong>acts on any objects which have mass <\/strong>and is always attractive<\/strong>.<\/p>\n

    Newton’s law of gravitation <\/strong>states that the magnitude of the gravitational force between two masses is directly proportional to the product of the masses, and is inversely proportional to the square of the distance between them, (where the distance is measured between the two centres of the masses).<\/p>\n

    F= m<\/em><\/strong>1<\/em><\/strong>m<\/em><\/strong>2\/<\/em><\/strong>r2<\/em><\/strong><\/p>\n

    Where G <\/em>is the gravitational constant, m1<\/sub>\/m2<\/sub> are masses and r <\/em>is the distance between the centre of the masses.<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

    It is important to note that the mass of a uniform sphere is considered to act as a point mass at its centre <\/strong>when calculating the gravitational force experienced by an object outside the sphere.<\/p>\n

    The gravitational field strength (g) <\/strong>in a radial field <\/strong>follows the equation<\/p>\n

    g= GM\/r2<\/sup><\/em><\/p>\n

    Where G is the gravitational constant, M is the mass of the object causing the field and r is the distance between the centre of the masses.<\/p>\n

    As you can see the field strength follows an inverse square relationship<\/strong>, meaning that if its distance increases by a factor of 2, the field strength will decrease by a factor of (22<\/sup> =) 4 as seen in the equation.<\/p>\n

    Objects, like satellites, orbit around masses due to their gravitational fields as the gravitational force exerted on the object acts as a centripetal force<\/strong>, which causes a centripetal acceleration <\/strong>causing them to move in a circle.<\/p>\n

    Gravitational Potential and Potential energy:<\/strong><\/p>\n

    The Potential energy of an object under the influence of a conservative force may be defined as the energy stored in the body and is measured by the work done by an external agency in bringing the body from some standard position to the given position. If a force F displaces a body by a small distance dr against the conservative force, without changing its speed, the small change in the potential energy dU is given by,<\/p>\n

    dU = –F.dr<\/p>\n

    In case of the gravitational force between two masses M and m separated by a distance r,<\/p>\n

    \"\"<\/p>\n

    ∴<\/em> gravitational potential energy<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

     <\/p>\n

    It shows that the gravitational potential energy between two particles of masses M and m separated by a distance r is given by<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

    The gravitational potential energy is zero when r approaches infinity. So, the constant is zero and<\/p>\n

    \"\"<\/p>\n

    The Gravitational Potential (V) <\/strong>of mass M is defined as the gravitational potential energy of the unit mass. Hence, Gravitational potential,<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

     <\/p>\n

    It is a scalar quantity and its SI unit is J\/kg.<\/p>\n

     <\/p>\n

    Contact forces:<\/strong><\/p>\n

    Contact forces are the forces that act between two objects in contact with each other. These forces arise due to the interaction between the molecules of the two objects at the point of contact. The magnitude and direction of contact forces depend on various factors such as the nature of the surfaces in contact, the force applied, and the angle of contact.<\/p>\n

    Some common examples of contact forces are:<\/p>\n

    Frictional force:<\/strong> This force arises due to the interaction between the surfaces of two objects in contact when they move or try to move relative to each other. Frictional force opposes the motion and is proportional to the normal force exerted by the objects on each other.<\/p>\n

    Normal force:<\/strong> This force is perpendicular to the surface of contact and arises due to the repulsive interaction between the molecules of the two objects in contact. The normal force is equal in magnitude and opposite in direction to the force applied by one object on the other.<\/p>\n

    Tension force:<\/strong> This force arises when an object is pulled or pushed by a rope, cable, or any other material in tension. The magnitude of the tension force is equal to the force applied by the material on the object.<\/p>\n

    Elastic force:<\/strong> This force arises when an object is deformed or compressed by another object. The magnitude of the elastic force is proportional to the deformation or compression.<\/p>\n

    Shear force:<\/strong> This force arises when two objects slide past each other in opposite directions. The magnitude of the shear force is proportional to the area of contact and the force applied.<\/p>\n

    Understanding contact forces is important in various fields such as physics, engineering, and material science.<\/p>\n

    Frictional Force<\/strong><\/p>\n

    Frictional force comes into play between two surfaces whenever there is relative motion or a tendency of relative motion between two surfaces in contact. The frictional force has the tendency to oppose relative motion between the surfaces in contact.<\/p>\n

     <\/p>\n

    Thus, friction can be classified as<\/p>\n

    (a) Static Friction: which acts between surfaces in contact but not in relative motion, it opposes the tendency of relative motion<\/p>\n

    (b) Kinetic Friction: which acts between surfaces in contact which are in relative motion, it opposes the relative motion between the surfaces.<\/p>\n

    Laws of Static Friction:<\/strong><\/p>\n

    Static Friction, acting between the surfaces in contact, (not in relative motion) opposes the tendency of relative motion between the surfaces.<\/p>\n

    It is independent of the area of contacting surfaces.<\/p>\n

    Now, fs(max) <\/sub>  µ N     where f\uf06c<\/sub><\/em> <\/sub> = fs(max)<\/sub><\/p>\n

                fs(max) <\/sub> = ms<\/sub>N<\/p>\n

    Here ms<\/sub> = coefficient of static friction.<\/p>\n

    N = normal reaction on the block from the surface.­<\/sub><\/em><\/p>\n

    When F exceeds f\uf06c<\/sub><\/em> <\/sub>block starts moving and frictional force decreases to a constant value fk<\/sub>. fk<\/sub> is called kinetic friction and it has a unique value which is given by<\/p>\n

                  fk<\/sub> = mk<\/sub> N<\/p>\n

    Here   mk<\/sub> = coefficient of kinetic friction.<\/p>\n

                N = normal reaction.<\/p>\n

    Angle Of Friction<\/strong><\/p>\n

    \"\"<\/p>\n

    The angle made by the resultant reaction force with the vertical (normal reaction) is known as the angle of friction.<\/p>\n

    The angle of Response:<\/strong><\/p>\n

     <\/p>\n

    \"\"<\/p>\n

    Consider a body of mass m resting on an inclined plane of inclination. The forces acting on the body are shown – Ff<\/sub> being the force of friction. If friction is large enough, the body will not slide down.<\/p>\n

     <\/p>\n

    Along x:     mg sin q – f = 0                              …(1)<\/p>\n

    Along y:     N –mg cosq = 0                              …(2)<\/p>\n

             i.e.    N = mg cos q and f = mg sin q<\/p>\n

     <\/p>\n

    or, tan q £ mS<\/sub>, the coefficient of static friction between the two surfaces, in order that the body doesn’t slide down. When q is increased so that<\/p>\n

    tan q > m, then sliding begins, and the angle qr<\/sub>  = tan-1<\/sup> m, where sliding begins is known as the angle of repose.<\/p>\n

     <\/p>\n

    Example 1:   A mass M is split into two parts m and (M-m), which are then separated by a certain distance.  What ratio (m\/M) maximises the gravitational force between the parts.<\/strong><\/p>\n

     <\/p>\n

    Solution: <\/strong>If r is the distance between m and (M-m), the gravitational force will be<\/p>\n

    \"\"<\/p>\n

    Example 2: <\/strong>A block weighing 2kg rests on a horizontal surface. The coefficient of static friction between the block and surface is 0.40 and kinetic friction is 0.20.<\/p>\n

             (a)How large is the friction force acting on the block?<\/p>\n

             (b)How large will the friction force be if a horizontal force of 5N is applied on the block?<\/p>\n

             (c)What is the minimum force that will start the block in motion?<\/p>\n

     <\/p>\n

    Solution:<\/strong>(a) As the block rests on the horizontal surface and no other force parallel to the surface is on the block, the friction force is zero.<\/p>\n

    (b) With the applied force parallel to the surfaces in contact 5N, opposing friction becomes equal and opposite. Further, the limiting friction is ms<\/sub>N = ms<\/sub>Mg = 8N<\/p>\n

          Force of friction is 5N.<\/p>\n

    (c) The minimum force that can start motion is the limiting one. ms<\/sub>N = ms<\/sub>mg = 8N<\/p>\n

                  <\/strong> <\/p>\n

     <\/p>\n

    Key point:<\/strong><\/p>\n

      \n
    • The gravitational field is the region of space around a massive object where the force of gravity is exerted on other objects.<\/li>\n
    • The strength of the gravitational field is determined by the mass of the object creating the field. The larger the mass, the stronger the field.<\/li>\n
    • Gravitational fields are described mathematically by the gravitational field equation, which states that the force per unit mass at a point in a gravitational field is equal to the gravitational field strength at that point.<\/li>\n
    • The gravitational field strength is a vector quantity, meaning it has both magnitude and direction. Its direction is always towards the center of the massive object creating the field.<\/li>\n
    • The gravitational field strength decreases with distance from the center of the massive object creating the field. This is described by the inverse-square law, which states that the strength of the field is inversely proportional to the square of the distance from the center of the object.<\/li>\n
    • Gravitational fields are not just created by massive objects like planets and stars, but also by any object with mass, no matter how small. This means that every object in the universe is surrounded by a gravitational field.<\/li>\n
    • Gravitational fields can cause the motion of objects to change, either by pulling them towards the massive object or by causing them to orbit around it. This is why the gravitational field of the Sun is so important for the orbits of the planets in our solar system.<\/li>\n
    • Gravitational fields can also cause the phenomenon of gravitational lensing, where light is bent as it passes through the field. This can result in distorted images of distant objects and is an important tool for astronomers studying the universe.<\/li>\n
    • The study of gravitational fields is an important part of both classical mechanics and general relativity and has profound implications for our understanding of the structure and evolution of the universe.<\/li>\n
    • Frictional force:<\/strong> This force arises due to the interaction between the surfaces of two objects in contact when they move or try to move relative to each other. Frictional force opposes the motion and is proportional to the normal force exerted by the objects on each other.<\/li>\n
    • Normal force:<\/strong> This force is perpendicular to the surface of contact and arises due to the repulsive interaction between the molecules of the two objects in contact. The normal force is equal in magnitude and opposite in direction to the force applied by one object on the other.<\/li>\n
    • Tension force:<\/strong> This force arises when an object is pulled or pushed by a rope, cable, or any other material in tension. The magnitude of the tension force is equal to the force applied by the material on the object.<\/li>\n
    • Elastic force:<\/strong> This force arises when an object is deformed or compressed by another object. The magnitude of the elastic force is proportional to the deformation or compression.<\/li>\n
    • Shear force:<\/strong> This force arises when two objects slide past each other in opposite directions. The magnitude of the shear force is proportional to the area of contact and the force applied.<\/li>\n<\/ul>\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

      Unit: Dynamics Chapter: Gravitational Field and Contact Forces Reference: AP Physics Algebra, Dynamics, Gravitational Field and Contact Forces, Gravitational Field, Gravitational field strength, Gravitational Force between Point Masses, Gravitational Potential and Potential energy, Contact forces, Frictional Force, Laws of Static Friction, Angle of Friction, The angle of Response After studying this chapter, you should be […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[622],"tags":[],"class_list":["post-9459","post","type-post","status-publish","format-standard","hentry","category-ap-physics-1"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=9459"}],"version-history":[{"count":0,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9459\/revisions"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=9459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=9459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=9459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}