## Ticket to Mars

Consider you are a space tourist with a round trip ticket to Mars. To board the shuttle at Earth’s sea level, there is a max weight requirement of 175 pounds. If the same requirement also exists to return home, what is the max weight (in lbs) you can weigh on Mars? Note the acceleration on Mar’s surface is 12.2 ft/s^2.

##
__
__**Hint**

**Hint**

Mass is how much matter exists inside an object. Weight is the force of gravity on an object.

##
__
__**Hint 2**

**Hint 2**

Newton’s 2nd Law:

$$$F=m\cdot a$$$

where
$$F$$
is the force,
$$m$$
is the mass, and
$$a$$
is the acceleration.

Mass is how much matter exists inside an object, and is typically measured in slugs. Weight is the force of gravity on an object, and is typically measured in pounds. On Earth, we colloquially use them interchangeably, but the two terms have distinctions for technical applications. The max weight of 175 lbs is actually providing the force. Because mass is constant throughout the universe but an object’s weight will depend on the gravitational environment, we need to first determine the requirement’s mass on Earth.

Newton’s 2nd Law:

$$$F=m\cdot a$$$

where
$$F$$
is the force,
$$m$$
is the mass, and
$$a$$
is the acceleration.

$$$175lb=m(32.2\frac{ft}{s^2})$$$

$$$m=\frac{175lb}{32.2\frac{ft}{s^2}}=5.4\frac{lb\cdot s^2}{ft}=5.4\:slugs$$$

Despite the acceleration due to gravity at the sea level on Earth is a higher
$$9.8\:m/s^2$$
compared to Mars, the mass requirement will be the same on both planets. Use Newton’s 2nd Law again to determine the equivalent weight requirement on Mars:

$$$F=(5.4slugs)(12.2\frac{ft}{s^2})=65.9\frac{slugs\cdot ft}{s^2}=65.9\:lbs$$$

65.9 lbs