Question

Saturn's mass is 5.68 x 1024 kg and its radius is 6.03 x 107 m. A. Calculate the gravitational field strength at Saturn's surface. (2 marks) B. Calculate the force of gravity at Saturn's surface on an object with a mass of 50 kg.

Answer 1

`\boxed {\boxed {\sf g=0.104 \ N/kg \ and \ F_g= 5.2 \ N }}`

Step-by-step explanation:

A. Gravitational Field Strength

The gravitational field strength can be calculated using the following formula:

`g= (Gm)/(r^2)`

G, or the universal gravitational constant, is 6.67 × 10⁻¹¹ N*m²/kg². The mass of Saturn is 5.68 × 10²⁴ kilograms. The radius of Saturn is 6.03×10⁷ meters.

Substitute these values into the formula.

`g= ( (6.67 * 10^(-11) \ N*m^2/kg^2) (5.68 * 10^(24) \ kg))/((6.03 * 10^(7) \ m )^2)`

Multiply the numerator and square the denominator.

`g= ( 3.78856 * 10^(14) \ N *m^2/kg )/(3.63609 * 10^(15) \ m^2)`

Divide.

`g= 0.1041932405 \ N/kg`

The original measurements of mass and radius have 3 significant figures, so our answer must have the same. For the number we found, that is the thousandth place. The 1 in the ten-thousandth place tells us to leave the 4 in the thousandth place.

`\boxed {g \approx 0.104 \ N/kg}`

B. Force of Gravity

The force of gravity is calculated using the following formula:

`F_g= mg`

The mass of the object is 50 kilograms. We just calculated the gravitational field strength, which is 0.104 Newtons per kilogram. Substitute these values into the formula.

`F_g= (50 \ kg)(0.104 \ N/kg)`

Multiply. The units of kilograms cancel.

`\boxed {F_g=5.20 \ N}`

Answer 2

Hi there!

A.

We can calculate the gravitational field strength using the following equation:

`g = (Gm_p)/(r^2)`

G = Gravitational Constant

mp = mass of planet (kg)

r = radius (m)

Plug in the given values:

`g = ((6.67*10^(-11))*(5.68*10^(24)))/((6.03*10^7)^2) = \boxed{0.104 N/kg}`

B.

The force can be calculated using:

`F_g = (Gm_1m_2)/(r^2)`

Plug in the values:

`F_g = ((6.67*10^(-11))(5.68*10^(24))(50))/((6.04*10^7)^2) = \boxed{5.209N}`