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The Problem: Identical Trucks and Their Mass
Two identical trucks, each with a mass of 2,104 kg, are parked 40 meters apart. The question is: how many times greater is the gravitational force between these two trucks compared to the weight of one truck? Assume the acceleration due to gravity, g = 9.8 m/s².
Detailed Solution: Calculating Gravitational Force
To solve this problem, we will step-by-step apply the formula and analysis to find the answer.
1. Calculating the Gravitational Force
According to Newton’s Law of Universal Gravitation, the gravitational force between two objects is calculated using the formula:
F = G * (m1 * m2) / r²
Where:
- F is the gravitational force between the two objects (N)
- G is the gravitational constant, G ≈ 6.674 × 10⁻¹¹ N(m/kg)²
- m1 and m2 are the masses of the two objects (kg)
- r is the distance between the centers of the two objects (m)
In this case:
- m1 = m2 = 2,104 kg (mass of each truck)
- r = 40 m (distance between the two trucks)
- G ≈ 6.674 × 10⁻¹¹ N(m/kg)²
Substituting the values into the formula, we get:
F = (6.674 × 10⁻¹¹) * (2,104 * 2,104) / (40)²
F ≈ 1.75 × 10⁻⁹ N
Therefore, the gravitational force between the two trucks is approximately 1.75 × 10⁻⁹ Newton.
2. Calculating the Weight of Each Truck
The weight of an object is the gravitational force of the Earth acting on that object. The formula for calculating weight is:
P = m * g
Where:
- P is the weight (N)
- m is the mass (kg)
- g is the acceleration due to gravity (m/s²)
In this case:
- m = 2,104 kg (mass of each truck)
- g = 9.8 m/s²
Substituting the values into the formula, we get:
P = 2,104 * 9.8
P = 20619.2 N
Therefore, the weight of each truck is 20619.2 Newton.
3. Comparing Gravitational Force and Weight
To find out how many times greater the gravitational force between the two trucks is compared to the weight of each truck, we perform the division:
Ratio = F / P = (1.75 × 10⁻⁹ N) / (20619.2 N)
Ratio ≈ 8.49 × 10⁻¹⁴
Thus, the gravitational force between the two trucks is only about 8.49 × 10⁻¹⁴ times the weight of each truck. This is an extremely small number, indicating that the gravitational force between objects with relatively small masses under normal conditions on Earth is negligible.
Conclusion
Through this problem, we see that although every object exerts a gravitational force on each other, for objects with relatively small masses and a relatively large distance, such as two trucks, this gravitational force is very small compared to the gravity that the Earth exerts on them. This explains why in daily life, we do not feel the gravitational force between objects around us, but only clearly feel the gravity of the Earth.
Hopefully, this article from Xe Tải Mỹ Đình has helped you better understand gravitational force and how to apply the formula to solve related problems.
