Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 16.4 N at a distance of 0.590 m from the hinges, and the second child pushes at a distance of 0.470 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.

F1 * d1 = F2 * d2.

16.4 * 0.590 = F2 * 0.470.
F2 = ?

To calculate the force that the second child must exert to keep the door from moving, we can use the principle of moments. The principle of moments states that for an object to remain in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.

First, we need to calculate the moment created by the first child's force. The moment is calculated by multiplying the force by the perpendicular distance from the pivot point (in this case, the hinges). Therefore, the moment created by the first child is given by:

Moment1 = Force1 * Distance1 = 16.4 N * 0.590 m

Next, we need to calculate the moment created by the second child's force. Similarly, the moment created by the second child is given by:

Moment2 = Force2 * Distance2

Since we want to find the force that the second child must exert to keep the door from moving, we can set the two moments equal to each other:

Moment1 = Moment2

16.4 N * 0.590 m = Force2 * 0.470 m

Simplifying the equation, we can solve for the force:

Force2 = (16.4 N * 0.590 m) / 0.470 m

Force2 ≈ 20.59 N

Therefore, the second child must exert a force of approximately 20.59 N to keep the door from moving.

To solve this problem, we need to find the net torque acting on the door and then determine the force required to counteract it.

Let's begin by calculating the torque exerted by each child.

Torque (τ) is given by the equation:
τ = force x perpendicular distance

For the first child:
τ1 = 16.4 N x 0.590 m

For the second child:
τ2 = force2 x 0.470 m

Since both children push in opposite directions, we need to consider the direction of torques. We'll assume counterclockwise is positive and clockwise is negative.

The net torque can be calculated by taking the difference between the two torques:

Net torque = τ2 - τ1

Now, we need to find the force required to counteract this torque and keep the door from moving. The force required can be determined using the equation:

Force = Net torque / perpendicular distance

Here, the perpendicular distance is the distance of the second child from the hinges (0.470 m). Substituting the values, we get:

Force = (τ2 - τ1) / 0.470 m

Now, we can plug in the given values to calculate the force required:

Force = (force2 x 0.470 m - (16.4 N x 0.590 m)) / 0.470 m

Simplifying the equation, we have:

Force = (force2 - 16.4 N x 0.590 m / 0.470 m

Force = (force2 - 9.676 N) / 0.470 m

To solve for the force2, we can rearrange the equation:

force2 = Force x 0.470 m + 9.676 N

Plugging in the given value for the force and perpendicular distance, we can calculate the force2:

force2 = (Force x 0.470 m) + 9.676 N

Now, substitute the value of Force and calculate force2.