Question

Scientists aboard the International Space Station are threatened by a 2.8 kg meteor hurtling toward them at 5.4 x 103 m/s. They deploy an enormous rubber band to catch the meteor.

The rubber band stretches 193 m as it stops the meteor and saves the day. How much average force is applied to the meteor?

A) 3.8 x 104 N



B) 5.2 x 104 N



C) 1.3 x 105 N



D) 2.1 x 105 N



E) 4.7 x 106 N

Answer 1

Answer:

c) 1.3 X 10⁵ N

Explanation:

Step 1: From equation of motion; V² = U² +2as

where, U  and V are initial and final velocity respectively,

a is the acceleration and s is the distance traveled

(5400)² = 0² +2*a*193

a = (5400)²/ (386)

a = 75544.04 m/s²

Step 2: calculate the maximum force applied to the meteor

$F_{max} = m*a$

$F_{max} = 2.8*75544.04$ = 211,523.312 N

Step 3: calculate the average force applied to the meteor

$F_{avg} = \frac{1}{2}F_{max}$

$F_{avg} = \frac{1}{2}(211,523.312 N)$ = 105,761.7 N

$F_{avg} =$ 1.1 X 10⁵ N

The nearest option is C