The centers of a 15 kg lead ball and a 140 g lead ball are separated by 8.0 cm.
What gravitational force does each exert on the other? Answer: 2.2×10^−8 N
Now: What is the ratio of this gravitational force to the weight of the 140 g ball?
I don't know how to do this, I've tried it a hundred different ways and cant seem to get it. Help?
Divide your answer to the first part by m*g, where m = 0.14 kg and g = 9.81 m/s^2
Weight = 1.373 N
2.2*10^-8/1.373 = ?
Ah, trying to crunch those numbers, are we? Don't worry, I'll clown around and help you out!
To find the ratio of the gravitational force to the weight of the 140 g ball, we need to compare the two quantities. Let's break it down step by step:
First, recall that weight is the force acting on an object due to gravity. The weight of an object can be calculated using the formula:
Weight = mass × gravity
Now, considering the 140 g lead ball, we can find its weight by multiplying its mass (140 g) by the acceleration due to gravity (approximately 9.8 m/s²). Don't forget to convert grams to kilograms, as the units must match:
Weight of 140 g lead ball = (140 g / 1000) kg × 9.8 m/s²
Once you've calculated the weight of the 140 g ball, you can compare it to the gravitational force between the two balls.
The ratio of the gravitational force to the weight of the 140 g ball will be:
Ratio = Gravitational force / Weight of the 140 g ball
Now, if you've already calculated the gravitational force correctly as 2.2×10^−8 N, you can simply divide it by the weight of the 140 g ball to find the ratio.
Give it another try, and remember to double-check your calculations. And hey, if those numbers are still playing hard to get, just give me a shout, and I'll bring out some funny math jokes to lighten the mood!
To find the ratio of the gravitational force to the weight of the 140 g ball, we need to calculate the weight of the 140 g ball first.
1. Weight is given by the formula: weight = mass × gravitational acceleration.
The mass of the 140 g ball is 0.140 kg (since 1 kg = 1000 g).
2. The gravitational acceleration is approximately 9.8 m/s² on the surface of the Earth.
Now, we can calculate the weight of the 140 g ball:
weight = mass × gravitational acceleration
= 0.140 kg × 9.8 m/s²
= 1.372 N (rounded to three decimal places)
The gravitational force between the two balls is given as 2.2×10^−8 N.
Finally, we can find the ratio:
ratio = gravitational force / weight
= (2.2×10^−8 N) / (1.372 N)
= 1.60×10^−8 (rounded to two decimal places)
Therefore, the ratio of the gravitational force to the weight of the 140 g ball is approximately 1.60×10^−8.
To find the ratio of the gravitational force between the two balls to the weight of the 140 g ball, we need to calculate the weight of the 140 g ball first.
The weight of an object is given by the formula:
Weight = mass × gravitational acceleration
Let's calculate the weight of the 140 g ball using this formula.
Given:
Mass of the 140 g ball = 140 g = 0.14 kg
Gravitational acceleration, denoted as 'g' = 9.8 m/s^2 (approximately)
Weight of the 140 g ball = 0.14 kg × 9.8 m/s^2 = 1.372 N (approximately)
Now we have the weight of the 140 g ball as 1.372 N.
To find the ratio of the gravitational force between the two balls to the weight of the 140 g ball, we divide the gravitational force by the weight of the 140 g ball.
Ratio = Gravitational force / Weight of the 140 g ball
Given:
Gravitational force = 2.2 × 10^−8 N (as mentioned in the question)
Using the given values:
Ratio = (2.2 × 10^−8 N) / (1.372 N) = 1.6 × 10^−8
Therefore, the ratio of the gravitational force between the two balls to the weight of the 140 g ball is approximately 1.6 × 10^−8.
Fnet = (mMG)/r^2
G= 6.67x10^-11 N.m^2/kg^2
r=8.0cm = 0.08m
M=140g = 0.140kg
m=15kg
F = (15kg x 0.140kg x 6.67x10^-11 N.m^2/kg^2)/ (0.08m)^2
F = 2.19x10^-8 N