Force and acceleration in object at rest

[blueberryfive]

Homework Statement

An object is at rest and stays at rest, but a rope attached to it is pulling with increasing force. What is the acceleration?

Homework Equations

F=ma

The Attempt at a Solution

The solution is that acceleration is constant and 0. Obviously a= dv/dt =0, since the object is at rest.

But if force is increasing, since F=ma, isn't acceleration increasing as well?

This is probably a stupid question, but I'm confused

 

[barryj]

Consider a block of wood on a table. As you gradually start pulling, or pushing, on the block, the force will obviously increase but the friction force will be equal to and opposite the force you are applying up to a maximum value. When the friction force is exceeded, then the block will accelerate according to F = ma where F is the net force on the block. The net force will be the force you are pulling with minus the friction force. Then there will be acceleration.

 

[blueberryfive]

Thanks, so I guess my problem is that F is the net force, not just the pulling force applied to the block.

 

[barryj]

That is correct.

 

[Nickie]

.

Your understanding is correct. As the force increases, the acceleration will also increase. However, since the object is initially at rest and remains at rest, the acceleration will still be 0. This is because there is an equal and opposite force acting on the object, balancing out the force of the rope and keeping the object in a state of equilibrium. So even though the force is increasing, the acceleration remains at 0 because there is no net force acting on the object. It is important to remember that the relationship between force and acceleration is not always linear and can be affected by other factors, such as the presence of other forces.