# Two objects, and where they meet

• ex81
In summary, a worker with a mass of Mw pulls on a mass-less rope attached to a box with a mass of mb on a friction-less surface. The worker pulls with a constant force starting at rest. The worker is at x = 0, and the box is at xb. The tension in the rope is external to the system, so the force on each object is equal. The worker and block move towards each other until they meet at xf. The displacement of time is equal to the displacement of the block from the initial position of the worker.
ex81

## Homework Statement

A worker with a mass of Mw is pulling on a mass-less rope that is attached to a box with a mass of mb on a friction-less surface. The worker pulls with a constant force starting at rest. The Worker is at x = 0, and the box is at xb Find the position at which they meet in terms given.

## Homework Equations

x = xi + vi * t + 1/2 a * t2
F = m * a

## The Attempt at a Solution

Using Newton's laws I know that the force on each object is equal, so

Fw = Fb

xw f = xw i + vw i* t + 1/2 a * t2

thus for the worker's side of the equation
xw f = 1/2 a * t2

and the box moves

xb f = xb i + vb i* t - 1/2 a * t2

thus

xb f = xb i - 1/2 a * t2

since they meet xb f is equal to xw f

thus

1/2 a * t2 = xb i - 1/2 a * t2

xb i = 1/2 aw * t2 + 1/2 ab * t2

2 xb i = (aw + ab) * t2

t = √( ( 2 * xb i) / aw + ab)

then taking what I have just solved for time, and plugging that back into the basic kinematic equation to find the distance I get jibberish. So I'm not sure where to go from here.

xmeet = xinitial + 1/2 aworker * ( ( 2 * xb i) / aw + ab)

They don't have the same acceleration, do they?
But do you really need to go through this?
Have you learned about center of mass?

Okay, your approach could work eventually, but the problem is that you don't know what your acceleration is, since you aren't given the force with which the worker pulls. There's a simpler way to go about this though. Think about the worker-block system. Is the tension in the rope external or internal to this system?

Using Newton's laws I know that the force on each object is equal, so

Fw = Fb
Use F=m•a to determine the acceleration of each of the bodies.

fun mass calculations

I know the force on the person, and block is the same but I do not know the mass, or ratio of mass. So the closest I can get to knowing the constant accelerations is a = F/mworker/block depending on which mass is used.

While I know about the center of mass, it isn't something I am supposed to use. Nor would it be okay to use as it is not a given, or something simple as a kinematic equation.

Last edited:
ex81 said:
I know the force on the person, and block is the same but I do not know the mass, or ratio of mass. So the closest I can get to knowing the constant accelerations is a = F/mworker/block depending on which mass is used.
That's right. The two bodies experience different accelerations.

If you don't use center of mass (by the way, you don't have to be "given" it to be able to use it) then your approach can work. However, with the answer you have you have it in terms of acceleration, but you want to have it in terms of only things given in the problem, so replace the accelerations by force and mass.

relative displacement and velocity concept would be nice here.
What would be the relative displacement of the man wrt the box, taking origin to be at the initial position of the man ?

@jack per the question I actually have to be given that to use it, or the answer is not correct. The whole if your method does not match it is not correct issue.

@phoenix The worker starts at x, which happens to be zero, and the box starts at x b. They meet at xf, and x box final(the same spot). Now this occurs at the same instant so the displacement of time delta T is therefore equal. My "solutions" just don't work.

Just replace the accelerations in terms of the known masses.and the tension in the rope.
The tension will simplify.

## 1. What is meant by "two objects"?

"Two objects" refers to any two physical entities that may come into contact with each other, such as two people, two cars, or two planets.

## 2. How do you determine where two objects will meet?

The meeting point of two objects can be determined by analyzing their trajectories and properties, such as their speed, direction, and gravitational pull on each other.

## 3. What factors can affect where two objects meet?

The factors that can affect where two objects meet include their initial positions, velocities, masses, and any forces acting upon them, such as gravity or friction.

## 4. Can two objects meet at multiple points?

Yes, two objects can meet at multiple points depending on their movements and the forces acting on them. For example, two planets may have multiple points of intersection in their orbits around each other.

## 5. What is the significance of knowing where two objects will meet?

Knowing where two objects will meet can help predict and prevent potential collisions or interactions between the objects. It can also provide insight into the behavior and properties of the objects and their surroundings.

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