Objects in equilibrium problem

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In summary, the problem involves a uniform plank with a length of 6 m and a mass of 30 kg resting horizontally on a scaffold, with 1.5 m of the plank hanging over one end. The question is how far a 70 kg person can walk on the overhanging part before the plank tips. To solve this, we make the pivot point at the point of overhang and calculate the torque needed to lift the bar. Using the equation T = F*d, we get a torque of 450 N*m. We then use the sum of torque formula, -450 + 700*x = 0, to solve for x and get the answer of 0.643 m.
  • #1
BrainMan
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The problem is a uniform plank of length 6 m and mass 30 kg rests horizontally on a scaffold, with 1.5 m of the plank hanging over one end of the scaffold. How far can a 70 kg person walk on the overhanging part of the plank before it tips?

Relevant equations
Sum of all the forces = 0
Sum of the torque must= 0Attempt-
(1) I make the pivot point at the point of overhang so 1.5 of of the board is over the pivot point and -4.5 is to the left of the pivot point.
(2) 1.5 is .25 of the length so it is .25 of the mass so the mass over the pivot point is 7.5. 4.5 is .75 of the length so it is .75 of the mass so the mass to the left of the pivot point is 22.5 kg.
(3) since the sum of all the torque is 0 then 22(-4.5)+7.5(1.5)+70(x)= 0
(4) solving for x I got 1.29 the correct answer is 0.643.
 
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  • #2
First you calculate the torque you need to lift the bar
Torque=F*d then T=300 * 1.5 = 450 N*m
now you do sum of the torque must be = 0
-450 + 700 *x = 0
solve for x = 0,643
 
  • #3
What do you mean by "lift" the bar?
 
  • #4
Tip the plank down. my bad xD
 
  • #5
Ok I understand. Where did you get the 300 in calculating the torque needed to lift the bar?
 
  • #6
its 30kg * 10 m/s²
 
  • #8
Ok thanks a lot!
 

Related to Objects in equilibrium problem

1. What is meant by "objects in equilibrium"?

"Objects in equilibrium" refers to a state where the net force acting on an object is zero, resulting in a balanced system. This means that the object is not accelerating and is either at rest or moving at a constant velocity.

2. How is equilibrium achieved?

Equilibrium is achieved when the sum of all forces acting on an object is equal to zero. This can happen when there are no external forces acting on the object, or when the forces acting on the object are balanced and cancel each other out.

3. What are the different types of equilibrium?

There are three types of equilibrium: stable, unstable, and neutral. In stable equilibrium, the object returns to its original position after a small displacement. In unstable equilibrium, the object moves away from its original position after a small displacement. In neutral equilibrium, the object remains in its new position after a small displacement.

4. How is equilibrium related to Newton's laws of motion?

Equilibrium is closely related to Newton's laws of motion. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. This is applicable to objects in equilibrium as they are either at rest or in constant motion. The second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. In equilibrium, the net force is zero, so the object is not accelerating. The third law states that for every action, there is an equal and opposite reaction. This means that in a balanced system, the forces acting on an object are equal and opposite, resulting in equilibrium.

5. How is equilibrium used in real-life applications?

Equilibrium is used in various real-life applications, such as building structures, bridges, and machines. Engineers and architects use the principles of equilibrium to design stable and strong structures that can withstand external forces. Equilibrium is also important in determining the stability of objects, such as balancing a seesaw or a bicycle. It is also used in chemistry to determine the concentration of solutions and in economics to analyze supply and demand.

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