# What is the force exerted by each hinge on the door?

• kamhogo
In summary, the door has a mass of 30 kg, two hinges that exert 294 N of torque each, and a lever arm of 1.5 m.
kamhogo

1. Homework Statement

The door has a mass of 30 kg, is 200 cm long and 90 cm wide. The hinges are installed at 25 cm from the bottom (R2) and 25 cm from the top (R1). What are is the magnitude of the force exerted by each hinge on the door? The door is in a state of static equilibrium.

## Homework Equations

Torque = rFsinθ
∑Torque = 0 Nm
∑F = 0
Fg = 30kg*9.8m/(s^2) = 294 N

## The Attempt at a Solution

a) Place pivot midway between hinges.
⇒F1 and F2 exert no torque (Parallel to axis or rotation).
⇒ F1+F2 = Fg = 294 N. No way to find each force individually.

⇒Lever arm for R1 = 0.75 m, θ = 90°; same for R2
Since ∑Torque = 0 Nm; Torque by R1 = Torque by R2 (opposite sign), so they must exert the same force (opposite sign) on the door.

I thought it might have been easier to place the "pivot" on one of the hinges.

kamhogo said:
Since ∑Torque = 0 Nm; Torque by R1 = Torque by R2 (opposite sign), so they must exert the same force (opposite sign) on the door.
It appears that you are assuming that the only forces that exert torques about your chosen pivot point are the forces R1 and R2. Would the weight force exert a torque about this pivot point?

I agree with Tom that placing the pivot point at one of the hinges is a good choice.

Keep in mind that ΣF = 0 applies to both the horizontal components and to the vertical components of the forces. That is, you have two equations ΣFx = 0 and ΣFy = 0.

So I just tried placing the pivot at the upper hinge and I think I got it:

Torque of Fg = 0.45m*294N*sin90°=132.3 Nm
Torque of Fg is opposed by Torque of R2, so Torque R2 = 132.3 Nm, lever arm = 1.5m, so R2 = 88.2 N = R1Thanks a lot :)

## 1. What is the definition of force?

Force is a physical quantity that describes the interaction between two objects and results in a change in their motion or shape.

## 2. How is the force exerted by each hinge on the door measured?

The force exerted by each hinge on the door can be measured using a force sensor or by calculating the torque applied by the hinge on the door.

## 3. What factors affect the force exerted by each hinge on the door?

The force exerted by each hinge on the door is affected by the weight of the door, the distance between the hinges, and the angle at which the door is opened.

## 4. How does the direction of the force exerted by each hinge on the door affect its movement?

The direction of the force exerted by each hinge on the door determines the direction in which the door will move. If the force is exerted in the same direction as the door's movement, it will open. If the force is exerted in the opposite direction, it will close.

## 5. Why is it important to consider the force exerted by each hinge on the door?

Understanding the force exerted by each hinge on the door is important for ensuring the door functions properly and for preventing damage to the hinges or the door. It also helps in determining the appropriate number and placement of hinges for a given door.

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