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A heavier mass m1 and a lighter mass m2 are 17.0 cm apart and experience a gravitational force of attraction that is 9.70 10-9 N in magnitude. The two masses have a combined value of 5.20 kg. Determine the value of each individual mass.

Sagot :

The value of m1 is 4.2 kg and value of m2 is 1 kg.

Computation of the value of m1 and m2:

Note:- The value of force is assumed to be 9.70*10^-9 N.

The gravitational force F is given by the formula,

F=Gm1m2 / r^2

where F is the force, G is the universal gravitational constant, m1 and m2 are masses and r is the distance between the masses.

Then the product of the masses is,

m1m2= Fr^2/G

Given F=9.70*10^-9 N, r is 17.0 cm which is equal to 0.17 m.

Therefore product m1m2= 9.70*10^-9 N *(0.17 m)^2 / 6.67*10^(-11) N m^2 kg^-2

m1m2= 4.20 kg^2

m1=4.20 kg^2/m2

The sum of masses is m1+m2=5.20 kg

 4.20/m2+m2=5.20

(m2)^2-5.20m2-4.20=0

After solving the above quadratic equation, mass m2 has values 4.2 kg and 1 kg.

By using m2=1 kg, m1 has greater mass 4.2 kg.

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Answer

m1 is equal to 4.2 kg and m2 is equal to 1 kg.

Explanation:

Note:- It is assumed that the force is equal to 9.70*10^(-9) N.

The force of gravitation F is calculated using formula,

F=Gm1m2/r^2

where G is the universal gravitational constant.

Given r=17 cm or 0.17 m and G=6.67*10^(-11) N m^2/ kg^2.

9.70*10^(-9)  = 6.67*10^(-11)*m1m2 / (0.17)^2

m1m2=4.20 kg^2

m1=4.20/m2

Given the sum of masses is 5.20 kg.

Therefore,

m1+m2=5.20

4.20/m2+m2=5.20

m2^(2)-5.20m-4.20=0

Solving the quadratic equation, m2 gives values 4.2 and 1.

By using these values, m1 gives values 1 and 4.2 respectively.

But m1 is greater than m2, so m2 =1 kg and m1 = 4.2 kg.

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