Question

1.A large beach ball weighs 4.0 N. One person pushes it with a force of 7.0 N due South while another person pushes it 5.0 N due East. Find the acceleration on the beach ball.

2. What is the weight of a 70 kg astronaut on the earth, on the moon, (g=1.6 m/s2), on Venus (g = 18.7 m/s2) and in outer space traveling at a constant velocity

Answer 1

1. force applied southward = -4 j

force applied eastward = 5 i

total force applied = 5i - 4j

magnitude of total force applied = √(5)²+(-4)²

magnitude of total force applied = √25 + 16 = √41

magnitude of total force applied = 6.4N

But the beach ball also weighs 4 N,

which means that a force of 4N is required to overcome the inertia of the ball

Net force applied on the ball = total force applied - force applied by inertia

Net force applied on the ball = 6.4 - 4

Net force applied on the ball = 2.4 N

Mass of the ball:

Mass of the ball = weight of the ball / gravitational constant

Mass of the ball = 4 / 9.8 = 0.4 kg

Acceleration of Ball:

from newton's second law of motion:

F = ma

replacing the variables

2.4 = 0.4 * a (where a is the acceleration of the ball)

a = 2.4/0.4

a = 6 m/s²

2. Mass of astronaut = 70 kg

Weight of Earth:

Weight = Mass * acceleration due to gravity

Weight = 70 * 9.8

Weight = 686 N

Weight on Moon:

Weight = Mass * acceleration due to gravity

Weight = 70 * 1.6 (we are given that g = 1.6 on moon)

Weight = 112 N

Weight on Venus:

Weight = Mass * acceleration due to gravity

Weight = 70 * 18.7 (we are given that g = 18.7 on Venus)

Weight = 1309 N