How can we obtain this equation?

[Lattes]

Homework Statement

A block of mass m rests on a horizontal surface. At t=0, a constant vertical force of magnitude F is applied to an ideal string attached to the block as shown. As a result, the block begins to move upward.

Answer all parts in terms of F, m, g, and t.

What is the velocity of the block as a function of time? Take upwards as positive.

Homework Equations

Power and Energy:
E = K + U;
Ef = Ei
Ef = Ei + W

The Attempt at a Solution

I can't get an answer through the equations involved, my attempts include only the kinematics equations, but they aren't working.

 

[berkeman]

Homework Statement

A block of mass m rests on a horizontal surface. At t=0, a constant vertical force of magnitude F is applied to an ideal string attached to the block as shown. As a result, the block begins to move upward.

Answer all parts in terms of F, m, g, and t.

What is the velocity of the block as a function of time? Take upwards as positive.

Homework Equations

Power and Energy:
E = K + U;
Ef = Ei
Ef = Ei + W

The Attempt at a Solution

I can't get an answer through the equations involved, my attempts include only the kinematics equations, but they aren't working.

Welcome to the PF.

Those aren't the relevant equations for this problem. You need to use the kinematic equations for a constant acceleration. Can you list those? The one for velocity as a function of acceleration and time is relevant, and another equation that relates force to acceleration.

 

[Lattes]

Welcome to the PF.

Those aren't the relevant equations for this problem. You need to use the kinematic equations for a constant acceleration. Can you list those? The one for velocity as a function of acceleration and time is relevant, and another equation that relates force to acceleration.

Thank you for guidance . I'll try again.

 

[PAllen]

Also, two of your equations, taken together, imply W=0, which is absurd. As a side exercise, think about what is wrong with the set as written.

 

[Lattes]

I understand and appreciate your comment, but these equations don't need to be used together, they are only part of the chapter I'm studying (potential energy and conservation of energy), so I published them as equations could be used. The fault was mine.

Anyway... thanks for your comment!

Yesterday a classmate gave me a new tip. He said I should do "a = F / m" and then integrate "a", but I still couldn't get v(t). I did...

a = F/m

v(t) = int(a) dt
v(t) = int(F/m) dt (F and m are constant)
v(t) = (F/m)int(dt)
v(t) = (F/m).t

But it isn't the answer of this problem. I don't know what to do.

 

[ehild]

Yesterday a classmate gave me a new tip. He said I should do "a = F / m" and then integrate "a", but I still couldn't get v(t). I did...

a = F/m

v(t) = int(a) dt
v(t) = int(F/m) dt (F and m are constant)
v(t) = (F/m)int(dt)
v(t) = (F/m).t

But it isn't the answer of this problem. I don't know what to do.

Is the applied force F is the only force acting on the block?

 

[Lattes]

Is the applied force F is the only force acting on the block?

The wording of the question mentions only F, but Weight is implied.

 

[The Vinh]

Before I write, I have to apologize for using English incorrectly if it really happens. I will assume that the initial velocity is Vo.
- the frame of reference is the ground.
- the conservation of energy: 0,5mV^2 + mgh = 0,5mVo^2
- the acceleration of substance: (F - P)/m = ( F/m - g) (F > P)
- the velocity of substance at time t:
V - Vo = (F/m - g)t <=> Vo = V - (F/m - g)t
- time - independent relation: V^2 - Vo^2 = 2(F/m - g)h <=> h = Vt - (t^2)/2 ( I have replaced Vo)
- I replace h and Vo => V = t/2 ( I cannot believe that this is the answer but I have checked again many times, I suggest you checking it again)

 

[barryj]

Don't make this into a hard problem. Acceleration = net force/mass. Notice that I said net force.
Once you have the acceleration, then the velocity = acceleration X time

 

[haruspex]

- the conservation of energy: 0,5mV^2 + mgh = 0,5mVo^2

F is an externally applied force, which adds energy.
As barryj writes, you are overcomplicating the problem.

 

[The Vinh]

Don't make this into a hard problem. Acceleration = net force/mass. Notice that I said net force.
Once you have the acceleration, then the velocity = acceleration X time

But i assume that the intial velocity is Vo, i don't want Vo = 0, what if in another circumstance, the system is provided with Vo

 

[haruspex]

But i assume that the intial velocity is Vo, i don't want Vo = 0, what if in another circumstance, the system is provided with Vo

Let's be completely clear about the problem you are trying to solve. Is it exactly the same as in the OP, except that the block has an initial upward velocity? If not, please start a new thread.

 

[The Vinh]

Let's be completely clear about the problem you are trying to solve. Is it exactly the same as in the OP, except that the block has an initial upward velocity? If not, please start a new thread.

Sorry, But what is the meaning of OP ?

 

[haruspex]

Sorry, But what is the meaning of OP ?

Original Post - the post which started the thread.

 

[The Vinh]

Original Post - the post which started the thread.

Oh, So if the block moves with zero intial velocity then the answer is V = (F/m - g)t . Just like BarryJ has said

 

[haruspex]

Oh, So if the block moves with zero intial velocity then the answer is V = (F/m - g)t . Just like BarryJ has said

Yes.