Gravitational Interactions » Truck and Car

In summary, to find the distance between a sports car and a cement truck given their masses and the force of attraction between them, use the formula r^2 = Gm_1m_2/F and then take the square root of the result.
  • #1
Sugi San
3
0

Homework Statement



i need help with this problem (Online HW)

If the force of attraction between a 1035 kg sports car and a 10680 kg cement truck is 3.930×10-6 N, how far are they apart?

Homework Equations



F = Gm_1m_2/r^2



The Attempt at a Solution

 
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  • #2
Where are you stuck? Rearrange that formula to solve for the distance r.
 
  • #3
r^2 = Gm_1m_2/F

We know m_1 = 1035, m_2 = 10680, F = 3.930 x 10^-6 and G is 6.67300 × 10^-11 m^3 kg^-1 s^-2.

So

r^2 = (6.67300 × 10^-11)(1035)(10680) / (3.930 x 10^-6)

= [(6.67300 )(1035)(10680) / (3.930)] x [10^-11/10^-6]
= [(6.67300 )(1035)(10680) / (3.930)] x 10^-5
= 18768958.6 x 10^-5
= 1876895.86 x 10^-6
= 1.87689586 x 10^-12

so how we find the distance?
 
  • #4
Sugi San said:
r^2 = (6.67300 × 10^-11)(1035)(10680) / (3.930 x 10^-6)

= [(6.67300 )(1035)(10680) / (3.930)] x [10^-11/10^-6]
= [(6.67300 )(1035)(10680) / (3.930)] x 10^-5
= 18768958.6 x 10^-5
OK.
= 1876895.86 x 10^-6
= 1.87689586 x 10^-12
You are messing up the exponents. When you move the decimal to the left one place you must add +1 to the exponent. You subtracted instead. (Example: 456.7 = 4.567 x 10^2)
so how we find the distance?
Once you correctly find r^2, just take the square root.
 
  • #5


To solve this problem, we can use the formula for gravitational force, F = Gm_1m_2/r^2, where G is the universal gravitational constant, m_1 and m_2 are the masses of the car and truck respectively, and r is the distance between them. We can rearrange the equation to solve for r, giving us r = √(Gm_1m_2/F). Plugging in the given values, we get r = √(6.674×10^-11 * 1035 kg * 10680 kg / 3.930×10^-6 N) = 1.432 meters. Therefore, the car and truck are approximately 1.432 meters apart.
 

FAQ: Gravitational Interactions » Truck and Car

What is the difference between gravitational interactions of a truck and a car?

The difference lies in the mass and size of the objects. The truck has a larger mass and size compared to the car, thus creating a stronger gravitational force on other objects.

How does the distance between the truck and car affect their gravitational interaction?

The gravitational force between the truck and car decreases as the distance between them increases. This is described by the inverse-square law, which states that the force is inversely proportional to the square of the distance between the objects.

Can gravitational interactions between a truck and car be observed on a small scale?

Yes, although the force may be very small, gravitational interactions can be observed between any two objects with mass, regardless of their size. However, the effects are more noticeable on a larger scale.

How does the gravitational force between a truck and car affect their motion?

The gravitational force between the truck and car will cause them to accelerate towards each other. This acceleration is dependent on the mass of the objects and the distance between them.

Is there a limit to the distance at which gravitational interactions between a truck and car can occur?

No, there is no limit to the distance at which gravitational interactions can occur. However, as the distance increases, the force becomes weaker and is eventually negligible.

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