Question

1. On Earth, the acceleration of gravity is about 10 m/s². What would it be on Mars, where Mars has radius that is nearly 0.53 Earth's, and a mass which is only 0.107 Earth's,

2. Suppose there is a box of books with a mass of 10 kg resting on a flat horizontal table, and that the coefficient of static friction between the table and the box is 0.5.

If you push on the box with a force of 60 newtons, will the box move?

Explain your answer.

Answer 1

1)

Acceleration due gravity on Earth, $g_{e}=GM_{e}/R_{e}^{2}$

Acceleration due gravity on Mars, $g_{m}=GM_{m}/R_{m}^{2}$

Given $g_{e}=10m/s^{2}$

$R_{m}=0.53R_{e}$

and $M_{m}=0.107M_{e}$

--------------------------------------

$g_{m}=GM_{m}/R_{m}^{2}$

$g_{m}=G*0.107M_{e}/(0.53R_{e})^{2}$

$g_{m}=G*0.107M_{e}/0.2809R_{e}^{2}$

$g_{m}=\frac{0.107}{0.2809}*GM_{e}/R_{e}^{2}$

$g_{m}=\frac{0.107}{0.2809}*g_{e}$

$g_{m}=\frac{0.107}{0.2809}*10m/s^{2}$

ANSWER: ${\color{Red} g_{m}=3.809m/s^{2}}$

==========================

2)

Here N is the Normal Reaction and Fr is the frictional Force

Applied Force =60 N

if Applied Force is larger than Frictional Force then the box will move

$Fr=\mu N$

$Fr=\mu mg$

$Fr=0.5*10kg*9.81m/s^{2}$

$Fr=49.05N$

$Applied\ Force>Fr$

ANSWER : The Box will move.

============================