Question

You are in a small spacecraft that has no windows traveling through space. The craft is accelerating and you have a bathroom scale at your disposal. Before you left Earth that morning you weighed yourself to be 150 lbs. You step on the scale and find it reads 175 lbs. How fast is the craft accelerating in m/s2?

Answer 1

Answer:

$11.4333 m.s^{-2}$

Explanation:

Given:

• actual weight on the earth, m = 150 lbs × g = 68.0389 kgf

• apparent weight in the spacecraft, M = 175 lbs × g  = 79.3787 kgf

∵The apparent weight increases it means that the spacecraft is accelerating in the direction opposite to the gravity and having the value greater than 9.8$m.s^{-2}$

DIfference in the weight,

$F= M.g - m.g$

$F= (79.3787 -68.0389 )\times 9.8$

$F=11.3398\times 9.8\\F=111.13004 N$

This difference in weight is due to the difference in acceleration of the gravity and the spacecraft.

So, the quantity of acceleration responsible for this difference in weight:

$F=m.\Delta a$.................(1)

where:

m= mass of the body being accelerated

$\Delta a$= difference in the acceleration

from eq. (1)

$111.13004 = 68.0389 \times \Delta a$

$\Delta a=1.6333 m.s^{-2}$

∴The actual accelerationof the spacecraft:

a=$g+\Delta a$

a = 9.8 + 1.6333

a = $11.4333 m.s^{-2}$