A student is about to do a push-up. Her

center of gravity lies directly above P on the
floor, which is 1.1 m from her feet and 0.4 m
from her hands.
If her mass is 55 kg, what is the force exerted by the floor on her hands? The acceleration of gravity is 9.81 m/s
2
.

Well, as a Clown Bot, I should say that doing push-ups can be quite the balancing act! Now, let's calculate the force exerted by the floor on her hands.

To find this force, we need to consider the moments about her feet and her hands. The moments (torques, if you want to get technical) should balance out since our student is in equilibrium.

Since her center of gravity is directly above P on the floor, we can treat her whole body as a single object with its weight concentrated at that point.

So, starting with the moment about her feet:
(mass) * (gravity) * (distance from feet to center of gravity) = (force on hands) * (distance from hands to center of gravity)

Plugging in the values:
(55 kg) * (9.81 m/s^2) * (1.1 m) = (force on hands) * (0.4 m)

Solving for the force on her hands:
(force on hands) = (55 kg * 9.81 m/s^2 * 1.1 m) / (0.4 m)

And the answer is... *drumroll*... the force exerted by the floor on her hands is approximately 1519.625 N.

Now, that's some serious force! But let's not forget the real challenge here: making sure she doesn't face-plant while doing those push-ups. Good luck to her!

To find the force exerted by the floor on her hands, we need to consider the forces acting on the student and use the concept of torque.

First, let's calculate the torque due to the gravitational force acting on the student's body. Torque is given by the formula:

Torque = force x distance

In this case, the force is the weight of the student, which is equal to her mass times the acceleration due to gravity:

Force = mass x acceleration due to gravity
Force = 55 kg x 9.81 m/s^2 = 539.55 N

Since the center of gravity is directly above point P, the distance between the center of gravity and the hands is 0.4 m. So the torque due to the gravitational force is:

Torque = Force x distance
Torque = 539.55 N x 0.4 m = 215.82 N·m

The torque due to the gravitational force is balanced by the torque exerted by the floor on the hands. The torque exerted by the floor is given by the formula:

Torque = Force on hands x distance between hands and center of gravity

We can rearrange the formula to solve for the force on the hands:

Force on hands = Torque / distance between hands and center of gravity

Plugging in the values:

Force on hands = 215.82 N·m / 1.1 m = 196.2 N

Therefore, the force exerted by the floor on her hands is approximately 196.2 N.

To find the force exerted by the floor on her hands, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

First, we need to find the net force acting on the student. The net force can be calculated as the product of the student's mass (55 kg) and the acceleration due to gravity (9.81 m/s^2). Therefore, the net force acting on the student is:

Net Force = Mass * Acceleration due to gravity
= 55 kg * 9.81 m/s^2

Next, we need to determine the distribution of this net force between the hands and the feet. Since her center of gravity lies directly above point P, which is 0.4 m from her hands and 1.1 m from her feet, we can calculate the weight acting on each point.

The weight acting on the feet can be calculated as:

Weight on feet = (Net Force) * (Distance to feet) / (Total distance)
= (55 kg * 9.81 m/s^2) * (1.1 m) / (1.1 m + 0.4 m)

Similarly, the weight acting on the hands can be calculated as:

Weight on hands = (Net Force) * (Distance to hands) / (Total distance)
= (55 kg * 9.81 m/s^2) * (0.4 m) / (1.1 m + 0.4 m)

Therefore, the force exerted by the floor on the hands is equal to the weight acting on the hands:

Force on hands = Weight on hands

Now, you can substitute the values in the above equation to find the force exerted by the floor on the student's hands.

While stationary, the total moment about an axis through her toes is zero.

Her hands are 1.5 m from her toes. Her center of mass is 1.1 m from her toes.

F*1.5 - M*g*1.1 = 0

F = (1.1/1.5)M*g = 395 Newtons