John weighs 660 N, and Marcia weighs 486 N. Estimate the gravitational force between them when they are 0.47 m apart.
I've tried finding the mass of john and marcia by doing m=F*a (F being their weight in Newtons and a being 9.8 m/s^2). When I found their masses, I applied them to the equation F=(Gmm')/r^2. However the answer I got was 4.74e^(-7) and it was incorrect.
I got
660/9.8 * 486/9.8 * 6.673E-11/.47^2 = 1.00891E-6
To estimate the gravitational force between John and Marcia, we can use Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Here's the step-by-step method to calculate the gravitational force:
1. Convert the weights of John and Marcia from Newtons to kilograms. You can do this by dividing their weights by the acceleration due to gravity (9.8 m/s^2).
John's weight in kg = 660 N / 9.8 m/s^2 = 67.35 kg
Marcia's weight in kg = 486 N / 9.8 m/s^2 = 49.59 kg
2. Calculate the gravitational force between them using the formula:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2), m1 and m2 are the masses of John and Marcia, and r is the distance between them.
Plugging in the values we have:
m1 = 67.35 kg
m2 = 49.59 kg
r = 0.47 m
G = 6.67430 x 10^-11 N(m/kg)^2
F = (6.67430 x 10^-11 N(m/kg)^2) * (67.35 kg) * (49.59 kg) / (0.47 m)^2
3. Perform the calculation:
F = 7.18277 x 10^-8 N
So, the estimated gravitational force between John and Marcia when they are 0.47 m apart is approximately 7.18277 x 10^-8 N.
It seems like there might have been a calculation mistake in your previous attempt, resulting in the incorrect answer.