"The mass of Venus is 81.5% that of..." was answered by our experts

High School
Physics
Force, Motion and Energy
Acceleration Due to Gravity

smellmovinglz

Answered question

2021-11-23

The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth.
(a) Compute the acceleration due to gravity on the surface of Venus from these data.
(b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venuse?

Answer & Explanation

Coldst

Beginner2021-11-24Added 18 answers

(a) The mass of Venus

M_{V}

represent 81.5% of the of the Earth. So, the mass of Venus is

M_{V}

=(81.5%)

M_{E}

(1)
Where

M_{E}

is the mass of the Earth. Plug the mass of Earth into equation (1), so we can get

M_{V}

M_{V} = (0.815) M_{E} = (0.815) (5.97 \times 10^{24} k g) = 4.86 \times 10^{24} k g

The radius of Venus represent 94.9% of the radius of the Earth. So, the radius of Venus is

R_{V} = (94.9 %) R_{E}

(2)
Where

R_{E}

is the radius of the Earth. Plug the radius of Earth into equation (2), so we can get

R_{V}

R_{V} = (0.949) (6.38 \times 10^{6} m) = 6.05 \times 10^{6} m

The weight w of a body is the total gravitational force exerted on it by all other bodies in the univerce where this gravitational force F is given by Newton`s general law of gravity by

F = G \frac{M_{V} m}{R_{V}^{2}}

(3)
Where

R_{V}

is the radius of Venus, m is the mass of the body. As we mentioned above, this gravitational force equals the weight of the body which is mg, so using equation (3) we get the acceleration on Venus by

m g = G \frac{M_{V} m}{R_{V}^{2}}

g v = G \frac{M_{V}}{R_{V}^{2}}

(4)
Now, we plug values for

R_{V}

M_{V}

and G into equation (4) to get gv

g v = \frac{G M_{V}}{R_{V}^{2}}

= \frac{(6.67 \times 10^{- 11} N \cdot m^{2} \div k g^{2}) (4.86 \times 10^{24} k g)}{{(6.05 \times 10^{6} m)}^{2}}

= 8.86 m \div s^{2}

Supoilign1964

Beginner2021-11-25Added 19 answers

(b) The mass doesnt

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