What force should the woman in Figure 9.45 exert on the floor
with each hand to do a push-up? Assume that she moves up at a
constant speed.
w(0.9) = 2F(1.5) I'm calling F for each hand and there are two of them
w = mg = 50(9.8) = 490
490(0.9) = 3F
F = 147 N for each hand
To determine the force required for the woman to do a push-up, we need to consider the forces acting on her.
In this case, we can assume that the woman's weight is acting vertically downward, denoted as W. To maintain a constant speed, the net force acting on her must be zero (no acceleration).
When she moves up at a constant speed, the reaction force provided by the floor, F_floor, should balance her weight. Since she is pushing off the floor with her hands, she needs to exert an equal and opposite force against the floor.
Therefore, the force the woman should exert on the floor with each hand to do a push-up is half of her weight or:
Force = Weight / 2
Keep in mind that the actual weight can vary depending on the person's body mass.
To determine the force that the woman exerts on the floor with each hand while doing a push-up, we need to consider the concept of force, specifically Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma).
In this case, since the woman is moving up at a constant speed, her acceleration can be considered zero. Therefore, the net force acting on the woman must also be zero because there is no change in velocity.
Since the net force is zero, the force exerted by the woman on the floor is equal in magnitude and opposite in direction to the force exerted by the floor on the woman. This is commonly referred to as the reaction force.
Therefore, the force that the woman exerts on the floor with each hand to do a push-up is equal to her weight. Weight is the force of gravity acting on an object and can be calculated using the formula W = mg, where "m" is the mass of the object and "g" is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
So, the force that the woman should exert on the floor with each hand to do a push-up is equal to her weight.