The gravitational force acting between the Earth and a 1500-kg car is approximately 14,000 Newtons. What would be the gravitational force acting between the Earth and a 3000-kg hippopotamus?(1 point)
Responses
7,000 Newtons
7,000 Newtons
56,000 Newtons
56,000 Newtons
14,000 Newtons
14,000 Newtons
28,000 Newtons
To determine the gravitational force acting between two objects, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 Nm^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.
In this case, we know that the gravitational force acting between the Earth and the 1500-kg car is approximately 14,000 Newtons. Let's denote the car's mass as m1 = 1500 kg.
Now, we need to find the gravitational force acting between the Earth and the 3000-kg hippopotamus. Let's denote the hippopotamus' mass as m2 = 3000 kg.
Since the Earth is the same for both cases, the distance (r) remains the same. The mass of the hippopotamus is twice that of the car, so we can expect the gravitational force to also be twice as large.
Applying the formula:
F = G * (m1 * m2) / r^2
F_hippo = G * (m1 * 2 * m1) / r^2
F_hippo = 2 * G * (m1 * m1) / r^2
Since F_car is approximately 14,000 Newtons, we can substitute it into the equation:
F_hippo = 2 * G * (m1 * m1) / r^2
F_hippo = 2 * G * (1500 kg * 1500 kg) / r^2
F_hippo = 2 * F_car
So, the gravitational force acting between the Earth and the 3000-kg hippopotamus will be twice as large as the gravitational force acting between the Earth and the 1500-kg car.
Therefore, the correct answer is 28,000 Newtons.