Four uniform spheres, with masses mA = 37 kg, mB = 30 kg, mC = 220 kg, and mD = 55 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (-77 cm, 0), and (44 cm, 0), respectively. Find the net force on sphere B due to the other spheres. What are the (a)x and (b)y components of that net force?
I cant figure out what in doing wrong! please help me :)
Post your work. I can't figure out what you are doing wrong either.
Im using the F=Gm1m2/r^2.
So to figure out the y i plugged in the values for massA and B and used a radius of .5 to get 2.96E-7.
For the x i used the same formula but did it twice once for particle CB and the other for BD. then i added them together and got -1.74E-7.
ok, you are not considering the forces to be vectors. Adding them as if they are in a straight line won't work. Sketch the locations, and then the forces have to be added as vectors. I would change each force to components in the x and y direction, then add the x's, to get the x sum, and then the same with the Fy.
Here is a similar (simpler) problem. Study it.
http://answers.yahoo.com/question/index?qid=20080331085912AASJv68
Thanks it worked :)
Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.500 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.50 µC. They are released from rest when their centers are separated by 1.00 m.
To find the net force on sphere B due to the other spheres, you need to calculate the gravitational forces between sphere B and each of the other spheres. The gravitational force between two objects is given by Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (approximately 6.674 × 10^(-11) N(m/kg)^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
To find the net force, you need to sum up the individual forces in both the x and y directions.
Here's a step-by-step guide to finding the net force on sphere B:
1. Calculate the distance between sphere B and each of the other spheres.
distance BA = √((0 - 0)^2 + (50 cm - 0)^2)
distance BC = √((-77 cm - 0)^2 + (0 - 0)^2)
distance BD = √((44 cm - 0)^2 + (0 - 0)^2)
2. Calculate the gravitational forces between sphere B and each of the other spheres using Newton's law of universal gravitation:
force BA = (G * mB * mA) / (distance BA)^2
force BC = (G * mB * mC) / (distance BC)^2
force BD = (G * mB * mD) / (distance BD)^2
3. Determine the direction of each force. Since sphere B is at the origin (0, 0), the direction of each force can be determined by the signs of their respective x and y coordinates.
4. Calculate the x and y components of each force by multiplying the magnitudes of each force by the cosine and sine of the angle of each force with respect to the x-axis.
5. Sum up the x and y components of each force to find the net force on sphere B.
6. Lastly, calculate the magnitude and direction of the net force in the x and y directions using the Pythagorean theorem and trigonometry.
I hope this helps! Let me know if you have any further questions.