A satellite is in a circular orbit around the Earth. If the radius of the orbit
Practice Questions
Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
7.9 m/s²
9.8 m/s²
11.2 m/s²
14.0 m/s²
Questions & Step-by-Step Solutions
A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
Step 1: Identify the formula for centripetal acceleration, which is a_c = v² / r.
Step 2: Note the values given: the speed (v) of the satellite is 7.9 km/s and the radius (r) of the orbit is 7000 km.
Step 3: Square the speed of the satellite: (7.9 km/s)² = 62.41 km²/s².
Step 4: Divide the squared speed by the radius: 62.41 km²/s² / 7000 km.
Step 6: Convert the result from km/s² to m/s² by multiplying by 1000 (since 1 km = 1000 m): 0.0089142857 km/s² * 1000 = 8.9142857 m/s².
Step 7: Round the result to two decimal places: 8.91 m/s².
Centripetal Acceleration – Centripetal acceleration is the acceleration directed towards the center of a circular path, necessary for an object to maintain its circular motion.
Circular Motion – Understanding the principles of circular motion, including the relationship between speed, radius, and acceleration.
Unit Conversion – Converting units correctly, especially between kilometers and meters, to ensure accurate calculations.
