What are the minimum force values needed to hold an object without it falling?

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In summary, the conversation discusses a physics problem involving a marble being held by a thumb and index finger. The minimum force values required to keep the marble from falling are determined by taking into account the mass of the marble, the force of gravity, and the coefficient of friction. The conversation also raises questions about the distribution of frictional force on each contact point.
  • #1
joedwagner
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This is a problem I came up without of curiosity but can't solve.. The image shows a situation similar to a thumb an index finger grasping a marble. Probably obvious to figure out, but I can't, so I'll ask. What are the minimum force values F1 and F2 necessary to keep the marble from falling if mass is known?
 

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  • #2
Start by drawing a correct free body diagram.:wink:
edit: Actually you still need a friction coefficient in order to solve it.
 
  • #3
Found a link saying the coefficient of friction is .05

So if the mass is M, the force of gravity on it would be mg, the force of friction must equal this so it would require a force of mg/.05 so for a marble weight .003kg, it would be .588N
 
  • #4
Force of friction is [itex] \mu N [/itex] where [itex] N [/itex] is the normal force. Since we also know that this needs to be [itex] \geq Mg [/itex] you can solve :)
As a side note I've included two frictional forces since there's no reason to assume one side is preferable to another and I know from experience there is no net torque, however if friction is independent of surface area would the force be distributed between the two contact points? In other words would each frictional force be half what I've written? It seems like it should be but how could each side "know" that the other side had some frictional force? Then again I guess it might have to since the same argument must be wrong when applied to any single atom "knowing" about the friction on any other atom with a block sliding down an incline.
I'll change the value back but leave this here as kind of an interest thing I guess. :)
 
  • #5


I would approach this problem by first considering the forces acting on the marble. The two main forces are the force of gravity pulling the marble downward and the force of the fingers pressing on the marble in an upward direction. In order to keep the marble from falling, the upward force from the fingers must be equal to or greater than the downward force of gravity.

The minimum force values F1 and F2 necessary to keep the marble from falling will depend on the mass of the marble and the strength of the fingers. This can be calculated using Newton's Second Law, which states that force is equal to mass times acceleration. In this case, the acceleration is equal to the force of gravity, which is 9.8 meters per second squared.

So, to calculate the minimum force values, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. Since we know the acceleration (9.8 m/s^2) and the mass of the marble, we can solve for the force.

For example, if the marble has a mass of 10 grams, the minimum force required to keep it from falling would be 0.098 Newtons (0.01 kg x 9.8 m/s^2 = 0.098 N). This would be the minimum force for each finger, so the total minimum force required to hold the marble would be 0.196 Newtons (0.098 N + 0.098 N = 0.196 N).

However, it's important to note that this is a simplified calculation and in reality, the minimum force values may be slightly higher due to factors such as friction and the strength and coordination of the fingers. Additionally, the shape and size of the object being held may also affect the minimum force values required. Therefore, it's always important to consider all factors and perform experiments to determine the exact force values needed in a specific situation.
 

What is a force?

A force is a push or pull exerted on an object that causes it to change its speed or direction of motion.

What are the different types of forces?

The main types of forces are contact forces (forces that result from physical contact between two objects) and non-contact forces (forces that act at a distance, such as gravity and magnetism).

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, while weight can vary depending on the gravitational pull of the surrounding environment.

How do forces hold an object in place?

Forces hold an object in place by counteracting the forces acting against it. For example, when you place an object on a table, the force of gravity is pulling it down, but the table exerts an equal and opposite force (normal force) upwards, keeping the object in place.

What factors affect the strength of forces holding an object?

The strength of forces holding an object depends on the mass of the object, the distance between the objects, and the type of force acting on it. For example, the force of gravity between two objects increases with their masses and decreases with the distance between them.

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