Lever and Acceleration: Greater Mass or Greater Accel?

In summary, the conversation discusses the relationship between the mass and length of the arms of a 10m lever with a center of mass 2m from the right side. It is noted that the shorter arm must have greater mass to maintain balance, but this does not necessarily mean it has a greater gravitational acceleration. The acceleration of gravity is the same for all masses and the lever must be in balance, so there cannot be a difference in acceleration. Additionally, in order to accelerate the lever, there must be an unbalanced torque. The linear and tangential acceleration may vary along the length of the arms due to geometry, but the difference in acceleration at equal lengths is negligible.
  • #1
ultrauser
23
0
If I have 10m lever with a center of the mass 2m from the right side it must mean the shorter arm have greater mass to keep balance. Does it mean longer (lighter) arm have greater gravitational acceleration cause it must travel greater distance in the same time ?
 
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  • #2
ultrauser said:
If I have 10m lever with a center of the mass 2m from the right side it must mean the shorter arm have greater mass to keep balance.
Only if it is in balance - a lever does not have to balance.

Does it mean longer (lighter) arm have greater gravitational acceleration cause it must travel greater distance in the same time ?
No.
1. the acceleration of gravity is the same for all masses anyway
2. since the two sides are in balance, the force due to gravity on both sides is the same - it cannot be accelerating: so you have a contradiction in your statement.

Notes:
In order to accelerate the lever, you need an additional unbalanced torque.
That torque causes the same angular acceleration in both arms.
The linear/tangential acceleration varies along the length of each arm - and is the same (with opposite sign) at equal lengths. The difference in linear accelerations of the endpoints is due to geometry.
 

1. How does the mass of an object affect its acceleration when using a lever?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. This means that if the mass of an object increases, its acceleration will decrease when using a lever.

2. Is it better to have a greater mass or a greater acceleration when using a lever?

It ultimately depends on the specific situation and goal. If the goal is to lift or move a heavy object, then a greater mass is preferred to generate a larger force. However, if the goal is to achieve a faster acceleration, then a smaller mass and greater force is needed.

3. How does the length of a lever affect its acceleration when using a greater mass?

The length of a lever does not directly affect its acceleration when using a greater mass. However, it does impact the amount of force needed to lift or move the object. A longer lever can provide a mechanical advantage, requiring less force to achieve the same acceleration as a shorter lever.

4. What is the relationship between the amount of force applied and the acceleration when using a lever?

The amount of acceleration produced by a lever is directly proportional to the amount of force applied. This means that if the force is increased, the acceleration will also increase, as long as the mass remains constant.

5. Can the use of a lever overcome the effects of greater mass?

Yes, the use of a lever can overcome the effects of greater mass by providing a mechanical advantage. By increasing the length of the lever or using a different fulcrum point, the lever can generate a larger force to overcome the mass and achieve the desired acceleration.

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