Forces on a hinged board used as a lever

In summary, the conversation is about a problem involving a 3 m board with a mass of 4.5 kg and a 75 kg block resting on it. A force F is applied at the end of the board to lift the block, which is 80 cm from the hinge. The questions ask for the force exerted by the hinge at a given angle and the magnitude of F when it is perpendicular to the board. The last question asks for the force exerted by the hinge in this scenario.
  • #1
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I'm having trouble with this one. Any help would be appreciated.

A 3 m board of mass 4.5 kg is hinged at one end. A force F is applied vertically at the other end to lift a 75 kg block, which rests on the board 80 cm from the hinge, as shown in Figure 12-35.

(b) Find the force exerted by the hinge at this angle. (in components)
(c) Find the magnitude of the force F if this force is exerted perpendicular to the board when = 30°.
(d) Find the force exerted by the hinge in this case (in components)
 
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Welcome to the Forums,

One is expected to show ones own efforts before requesting help.
 
  • #3


I would first clarify the setup and terminology used in the question. The board is being used as a lever, with the hinge acting as the fulcrum. The force F is being applied at the opposite end of the board to lift a block, which is positioned 80 cm from the hinge. The angle at which the force F is being applied is denoted as θ.

To solve part (b), we can use the principle of moments, which states that the sum of the moments (or torques) acting on a system must be equal to zero for the system to be in equilibrium. In this case, the hinge is acting as the fulcrum and the weight of the board and block are acting downwards, creating a clockwise moment. The force F is acting upwards, creating a counterclockwise moment. Therefore, we can set up the following equation:

Mhinge + Mboard + Mblock = 0

Since the board is hinged at one end, the moment of the hinge (Mhinge) is equal to zero. We can also assume that the weight of the board is negligible compared to the weight of the block, so the moment of the board (Mboard) can also be ignored. This leaves us with:

Mblock = F * d

Where d is the distance between the force F and the hinge, which in this case is 3 m – 0.8 m = 2.2 m. The moment of the block (Mblock) can be calculated as:

Mblock = (75 kg * 9.8 m/s^2) * 0.8 m = 588 Nm

Setting this equal to the moment of the force F, we can solve for the force F:

588 Nm = F * 2.2 m
F = 588 Nm / 2.2 m = 267.27 N

To find the force exerted by the hinge, we can use the law of cosines to find the magnitude of the force (FH) and the law of sines to find the angle (α) between the force and the horizontal:

FH^2 = F^2 + (75 kg * 9.8 m/s^2)^2 – 2 * F * 75 kg * 9.8 m/s^2 * cos(150°)
FH = 539.5 N

sin(α) = F
 

1. What is a hinged board used as a lever?

A hinged board used as a lever is a simple machine that consists of a long, rigid board (the lever) attached to a fixed point (the hinge) and used to lift or move objects.

2. How does a hinged board as a lever work?

A hinged board used as a lever works by using a downward force at one end of the board to produce an upward force at the other end. This is due to the principle of mechanical advantage, which allows the lever to amplify the input force and make it easier to move larger or heavier objects.

3. What are the different types of forces acting on a hinged board used as a lever?

The different types of forces acting on a hinged board used as a lever include the input force (applied at one end of the lever), the output force (produced at the other end of the lever), the fulcrum force (the pivot point of the lever), and the weight of the lever itself.

4. How does the position of the fulcrum affect the lever's mechanical advantage?

The position of the fulcrum on a hinged board used as a lever affects its mechanical advantage. Moving the fulcrum closer to the output end of the lever will increase the mechanical advantage, making it easier to lift heavier objects. Conversely, moving the fulcrum closer to the input end will decrease the mechanical advantage, requiring more input force to lift the same weight.

5. What are some real-world examples of hinged boards used as levers?

Some real-world examples of hinged boards used as levers include seesaws, crowbars, wheelbarrows, and scissors. These are all simple machines that use the principles of leverage to make tasks easier and more efficient.

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