Velocity and forces

1. Sep 13, 2009

MechaMZ

1. The problem statement, all variables and given/known data
time-dependent force, $$\vec{}F$$= (8.60i - 4.20tj) N (where t is in seconds) is applied to a 2.00 kg object initially at rest.

(a) At what time will the object be moving with a speed of 15.0 m/s?

3. The attempt at a solution

$$\vec{F}$$ = ma
$$\sqrt{8.6^2 + (4.20t)^2}$$ = 2a
a = $$\sqrt{8.6^2 + (4.20t)^2}$$ / 2

vf = vi +at
15 = 0 + [$$\sqrt{8.6^2 + (4.20t)^2}$$ / 2]t

this should be an easy question but I can't get the correct answer as 2.86s from the equations above, I can't figure out the reason. hope someone could enlighten me

2. Sep 13, 2009

rl.bhat

Check the last calculation.
Square both side.
225*4 = [8.6^2 + 4.2^2*t^2]*t^2
Solve for t.

3. Sep 13, 2009

MechaMZ

Hi,

I think even we square both side, the answer is still incorrect. you will get 2.36s but the answer is 2.86s.

I think the problem is because the vf = vi +at, gives you the instantaneous velocity yet the question requires you to find speed.

4. Sep 13, 2009

kuruman

Your method works only if the velocity is in the same direction as the acceleration at all times. This is not the case here because the x-component of the acceleration is constant while the y-component changes with time. You need to calculate vx(t) and vy(t) separately, then apply the Pythagorean theorem to get the speed as a function of time.

5. Sep 13, 2009

Staff: Mentor

The problem is that vf = vi + at applies to constant acceleration, which this is not. (Integrate each component separately.)

6. Sep 13, 2009

MechaMZ

Hi,

so what method should I use for the Vy?
however, I could still using vf = vi +at for Vx since it is a constant acceleration?
I was wondering the v in the equation above is for instantaneous velocity yet the question is asking about speed.

7. Sep 13, 2009

Staff: Mentor

That's not an issue. The instantaneous speed is just the magnitude of the instantaneous velocity.

8. Sep 13, 2009

MechaMZ

Hi Doc,

How about the question below, was the elevator accelerating with a constant value or not? may i know how did you know the a is constant or not?

any clue so that i could know the elevator is accelerating with a constant or not a constant value during the first 0.5s?

thank you

9. Sep 13, 2009

Staff: Mentor

Unless you are given information to the contrary, I would just assume that all accelerations are constant.

10. Sep 13, 2009

MechaMZ

but if i take 1.82/0.5 is the instantaneous acceleration or average acceleration or constant acceleration for each second from 0m/s to 1.82m/s?

11. Sep 13, 2009

Staff: Mentor

If you assume that the acceleration is constant, then all three of those are the same! (Since Vf = Vi + at.)

12. Sep 13, 2009

MechaMZ

argh, how about this question, why all my assumptions are wrong regarding the acceleration, force and velocity.

The figure below shows the speed of a person's body as he does a chin-up. Assume the motion is vertical and the mass of the person's body is 68.0 kg.

http://img147.imageshack.us/img147/5012/p527.gif [Broken]

(a) time zero
correct answer is 687 N, but i thought it should be 68x9.81=667.08

why?

Last edited by a moderator: May 4, 2017
13. Sep 13, 2009

kuruman

You don't say what the question is, but 68*9.81 N is the answer to "What is the person's weight?".

Last edited: Sep 13, 2009
14. Sep 13, 2009

Staff: Mentor

You didn't tell us your assumptions, so we can't say what's wrong.
Please post the exact question and your reasoning. I suspect the question asks for the force he exerts on the bar during the initial portion of the chin up. Since he's accelerating, the force must be greater than just his weight.

15. Sep 13, 2009

MechaMZ

Hi Doc,

the question is "Determine the force exerted by the chin-up bar on his body at the following times."

(a) time zero
correct answer is 687 N, but i thought it should be 68x9.81=667.08

I was thinking when the time is zero, the velocity(movement) is zero. so there is no any upwards resultant force. I assume the T-mg = 0, so T = mg - 68* 9.81.

please give me some clue on this, thank you =)

16. Sep 13, 2009

kuruman

The velocity may be zero, but his acceleration is not. Can you read the acceleration from the graph?

17. Sep 14, 2009

Staff: Mentor

The question is somewhat poorly worded. When he's just hanging, before he starts his chinup, the force exerted by the chinup bar equals his weight. But you need to base your answer on the given diagram. (Note that they don't show the time before he starts pulling.) They are treating t = 0 as when he's already started pulling. A better way to phrase the question would have been: Determine the force exerted by the bar immediately after he starts the chinup.

18. Sep 14, 2009

MechaMZ

i see, so there is an acceleration.