A 23.7 kg child, with a 4.35 kg backpack on his back, first stands on a sidewalk and then jumps up into the air. Find the net force (positive up/negative down) on Earth due to the child when the child is (c) standing still and (d) in the air.
To find the net force on Earth due to the child, we need to consider Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Let's consider the different scenarios:
(c) When the child is standing still on the sidewalk, we assume that the child and the backpack are not moving. In this case, the child and the backpack experience a net force of zero on Earth. This is because the force due to the child's weight and the force due to the backpack's weight cancel each other out. The gravitational force pulling the child and backpack downwards (negative direction) is counteracted by an equal and opposite force exerted by the ground (positive direction).
(d) When the child is in the air, the only force acting on the child and the backpack is due to their weights. The child and the backpack experience a gravitational force directed towards the center of the Earth. In this case, the net force is equal to the sum of the individual forces exerted by the child and the backpack, which can be calculated using the formula:
net force = (mass of child × acceleration due to gravity) + (mass of backpack × acceleration due to gravity)
Considering the mass of the child is 23.7 kg, the mass of the backpack is 4.35 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can substitute these values into the formula to obtain the net force on Earth.
net force = (23.7 kg × 9.8 m/s²) + (4.35 kg × 9.8 m/s²)
Evaluating this expression will give us the net force on Earth due to the child when the child is in the air.