A coordinate system (in meters) is constructed on the surface of a pool table, a
ID: 1430463 • Letter: A
Question
A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 10.0-kg object at the origin of the coordinate system, a 20.0-kg object at (0, 2.0), and a 28.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude N direction °A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 10.0-kg object at the origin of the coordinate system, a 20.0-kg object at (0, 2.0), and a 28.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude N direction °
magnitude N direction °
Explanation / Answer
Here ,
the gravitational force acting between two objects is given as
F = G * m1 *m2/d^2
where d is the distance between the objects
for the forces betweem 10 Kg and 20 Kg
F1 = 6.673 *10^-11 * 10 * 20/2^2 j
F1 = 3.34 *10^-9 j N
for the force between between 10 Kg and 28 Kg
F2 = 6.673 *10^-11 * 10 * 28/4^2 i
F2 = 1.168 *10^-9 i N
Now , for net force
magnitude of net force = sqrt(F1^2 + F2^2)
magnitude of net force = sqrt(3.34^2 + 1.67^2) *10^-9
magnitude of net force = 3.54 *10^-9 N
the magnitude of net force acting on the mass at origin is 3.54 *10^-9 N
direction = arctan(3.34/1.168)
direction = 70.7 degree
the direction of net force is 70.7 degree
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