A coordinate system (in meters) is constructed on the surface of a pool table, and
three objects are placed on the coordinate system as follows: a 1.5 kg object at the origin,
a 3.4 kg object at (0 m,1.8 m), and a 4.5 kg
object at (4.2 m,0 m).
Find the resultant gravitational force exerted on the object at the origin by the other
two objects. The universal gravitational constant is 6.672 × 10
−11
N · m2
/kg
2
.
Answer in units of N
Well, if we take the gravitational constant as seriously as it takes itself, we can calculate the gravitational force exerted on the object at the origin by the other two objects.
Let's call the mass of the object at the origin M1, the mass of the object at (0 m,1.8 m) M2, and the mass of the object at (4.2 m,0 m) M3.
The gravitational force between two objects is given by the equation:
F = (G * M1 * M2) / r^2
where G is the gravitational constant, M1 and M2 are the masses of the objects, and r is the distance between them.
So, let's calculate the force between the object at the origin and the object at (0 m,1.8 m). The distance between them is just the y-component, which is 1.8 m. Plugging in the values, we get:
F1 = (6.672 × 10^−11) * (1.5 kg) * (3.4 kg) / (1.8 m)^2
Now, let's calculate the force between the object at the origin and the object at (4.2 m,0 m). The distance between them is just the x-component, which is 4.2 m. Plugging in the values, we get:
F2 = (6.672 × 10^−11) * (1.5 kg) * (4.5 kg) / (4.2 m)^2
Now, to find the resultant force, we just need to add the two forces:
Resultant force = F1 + F2
Hope that helps! Remember, gravity is always there for you, pulling you down, even on a pool table!
To find the resultant gravitational force exerted on the object at the origin, we need to calculate the gravitational force between the object at the origin and the other two objects.
Gravitational force (F) between two objects can be calculated using the formula:
F = G * ((m1 * m2) / r^2)
Where:
F = gravitational force
G = universal gravitational constant (6.672 × 10^-11 N * m^2 / kg^2)
m1 = mass of the first object
m2 = mass of the second object
r = distance between the objects
Let's calculate the gravitational forces exerted on the object at the origin by the other two objects separately and then add them to find the resultant force.
1) Gravitational force between the object at the origin (mass = 1.5 kg) and the 4.5 kg object at (4.2 m,0 m):
Distance (r1) between the objects can be calculated using the distance formula:
r1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4.2 m - 0 m)^2 + (0 m - 0 m)^2)
= sqrt(4.2^2 + 0^2)
= sqrt(17.64)
≈ 4.2 m
Now, let's calculate the gravitational force (F1) exerted on the object at the origin by the 4.5 kg object:
F1 = G * ((m1 * m2) / r1^2)
= 6.672 × 10^-11 N * m^2 / kg^2 * ((1.5 kg * 4.5 kg) / (4.2 m)^2)
= 6.672 × 10^-11 N * m^2 / kg^2 * (6.75 kg^2 / 17.64 m^2)
≈ 2.5505 × 10^-10 N
2) Gravitational force between the object at the origin (mass = 1.5 kg) and the 3.4 kg object at (0 m, 1.8 m):
Distance (r2) between the objects can be calculated using the distance formula:
r2 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((0 m - 0 m)^2 + (1.8 m - 0 m)^2)
= sqrt(0^2 + 1.8^2)
= sqrt(3.24)
≈ 1.8 m
Now, let's calculate the gravitational force (F2) exerted on the object at the origin by the 3.4 kg object:
F2 = G * ((m1 * m2) / r2^2)
= 6.672 × 10^-11 N * m^2 / kg^2 * ((1.5 kg * 3.4 kg) / (1.8 m)^2)
= 6.672 × 10^-11 N * m^2 / kg^2 * (5.1 kg^2 / 3.24 m^2)
≈ 1.05016 × 10^-11 N
Now, let's find the resultant gravitational force (F_res) by adding the forces F1 and F2:
F_res = F1 + F2
= 2.5505 × 10^-10 N + 1.05016 × 10^-11 N
≈ 2.655516 × 10^-10 N
Therefore, the resultant gravitational force exerted on the object at the origin by the other two objects is approximately 2.655516 × 10^-10 N.
To find the resultant gravitational force exerted on the object at the origin, we need to calculate the gravitational force between each pair of objects and then determine their vector sum.
The formula for gravitational force between two objects is given by:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force between the two objects,
G is the universal gravitational constant (6.672 × 10^-11 N · m^2 / kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
First, let's calculate the gravitational force between the 1.5 kg object at the origin and the 3.4 kg object at (0 m, 1.8 m):
m1 = 1.5 kg
m2 = 3.4 kg
r = √((0 - 0)^2 + (1.8 - 0)^2) = 1.8 m
Plugging these values into the formula, we get:
F1 = 6.672 × 10^-11 * (1.5 * 3.4) / (1.8)^2
Next, let's calculate the gravitational force between the 1.5 kg object at the origin and the 4.5 kg object at (4.2 m, 0 m):
m1 = 1.5 kg
m2 = 4.5 kg
r = √((4.2 - 0)^2 + (0 - 0)^2) = 4.2 m
Plugging these values into the formula, we get:
F2 = 6.672 × 10^-11 * (1.5 * 4.5) / (4.2)^2
To find the resultant gravitational force, we need to determine the vector sum of these two forces. Since the objects are placed on a coordinate system, we can use the Pythagorean theorem to calculate the magnitude of the resultant force (F_resultant) and use trigonometry to find its direction.
The magnitude of the resultant force can be calculated as follows:
F_resultant = √(F1^2 + F2^2)
To find the direction of the resultant force, we can use the inverse tangent function (tan^-1) to determine the angle relative to the x-axis:
θ = tan^-1(F2 / F1)
Calculating these values will give us the answer in units of N.
Use Newton's law of gravity to calculate the two perpendicular forces acting on the object at the origin. Call them Fx and Fy
The force in the +y direction is
Fy = G*(1.5)*(3.4)/(1.8)^2
Write the equation for the other force, Fx, and then add Fx and Fy vectorially.