Newton's Second Law and Gravity

## Question:

I asked you for help on a Physics problem before, and your email was of great help to me. We are currently doing Forces combined with Centripetal acceleration, and I was wondering if you could possibly help me with a few homework problems that I have tried, but not understood. Any help would be greatly appreciated...

#1. The gravitational attraction between 2 identical spheres is 1 M apart (center to center) is 1 X 10^ -8 N. Calculate the mass of each sphere.

#2 What average force acts to enable a 4000 lb auto starting from rest to reach 60 MPH in 10 seconds?

#3How far from earth's surface would you have to have your weight reduced by 10%?

~* Again, thank you for your help*~

You need to have the practice of doing the homework problems but I can help you get started by illustrating the approach using these examples.

First decide what kind of problem it is. Then turn to your text book for the discussion of that kind of problem. Look for any equations that involve the information you are given and asked for. Insert the given information in the appropriate equation to solve for the unknown. In some problems this recipe may have to be repeated more than once to arrive at the final answer.

#1. This is a question involving gravity. In my textbook I find Newton's law of universal gravitation that looks sort of promising. It says F = G*m1*m2 / r^2. We are given that m1=m2, r=1 and that F=1e-8N. G is a constant that may be looked up in the book. Plugging this in I find 1e-8 = G*m*m / 1 or m^2 = 1e-8/G. Taking the square root of both sides I solve for m.

#2 Involves force and a change of speed, which is acceleration. In my textbook I find that Newton's second law seems to fit this situation. It says F=m*a. The problem is we are not directly given what we need. The given information needs to be manipulated a bit to fit the equation.

We need mass and acceleration but are given weight and change in velocity over time. Weight is a force due to gravitational acceleration so we can apply Newton's second law directly to get the mass. F = m*a or m=F/a = 4000/32.2 where 32.2 is the acceleration of gravity at Earth's surface in ft/s/s. This gives us a mass of 124.2 slugs.

Next we need to recognize that acceleration is the change in velocity divided by the time for that change. That is the definition of acceleration. Also to stay in a consistent set of units we need to convert the given velocity to ft/s. There are 5280 ft/mile and 3600 seconds per hour so we need to multiply the 60 mph by 5280 and divide it by 3600 to get 88 f/s. If you do not work in consistent units you are guaranteed to get the wrong answer. Now we can get the acceleration by a = (88-0)/10.

Finally we are ready to plug the given information, converted into appropriate units, into Newton's second law to get the answer. F = 124.2 * 8.8 = 1093 pounds force.

#3 seems like another gravity question. Newton's law of universal gravitation is still F = G*m1*m2/r^2. We know that weight is the force due to Earth's gravity on an object and for a given object the quantities G, m1 and m2 will all be constant. Weight then is inversely proportional to r^2. To reduce weight by 10% means that final weight, wf, divided by initial weight, wi, is wf/wi=0.9. But wf/wi is ri^2/rf^2 since weight is inversely proportional to r^2. So (ri/rf)^2 = 0.9 or ri/rf = 0.949 or rf = ri/0.949 = ri* 1.054. To decrease weight 10% then we need to increase our current distance from the center of any planet by a factor of 1.054.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ