A 33.4 kg child, with a 3.05 kg backpack on his back, first stands on a sidewalk and then jumps up into the air. Find the force (positive up/negative down) on the sidewalk from the child when the child is (a) standing still and (b) in the air. Now 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.
m = 33.4 kg +3.05kg = 36.45
Fup on child = 36.45*9.81 = 358 Newtons
so
a) Fdown on sidewalk = -358 Newtons
b) zero
c) -358 Newtons
d)zero
To find the force on the sidewalk and the net force on Earth, we need to consider Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
(a) When the child is standing still on the sidewalk, the force on the sidewalk is equal to the weight of the child and the backpack. The weight (force due to gravity) can be calculated using the formula:
Force = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the force on the sidewalk when the child is standing still is:
Force = (mass of child + mass of backpack) * acceleration due to gravity
= (33.4 kg + 3.05 kg) * 9.8 m/s^2
= 359.87 N (positive direction is upwards)
(b) When the child is in the air, the force on the sidewalk is zero because the child is not in contact with the ground. The child is experiencing a force due to gravity, but this force is balanced by the child's upward acceleration, resulting in a net force of zero on the sidewalk.
(c) When the child is standing still, the net force on Earth due to the child is equal to the weight of the child and the backpack. Since the child is not moving, the net force is also equal to zero according to Newton's first law of motion (an object at rest remains at rest unless acted upon by an external force).
(d) When the child is in the air, the net force on Earth due to the child is still equal to the weight of the child and the backpack. The weight (force due to gravity) is acting in the downward direction, so the net force on Earth is:
Net force on Earth = -(mass of child + mass of backpack) * acceleration due to gravity
= -(33.4 kg + 3.05 kg) * 9.8 m/s^2
= -359.87 N (negative direction is downwards)