Calculate tension if acceleration given

AI Thread Summary
To calculate the tension in a rope when a 70.0 kg man climbs vertically with an acceleration of 0.40 m/s², the formula T = m(g + a) yields a tension of 714 N when accelerating upwards. Conversely, if he slides down with the same acceleration, the formula T = m(g - a) results in a tension of 685 N. There is a discussion about the direction of gravitational force, with some suggesting that when moving upwards, gravity should be considered negative. The calculations are confirmed to be correct, and the conversation concludes with agreement on the results. Overall, the calculations for tension in both scenarios are validated.
bigman8424
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a 70.0 kb man climbs vertical rope attached to ceiling. weight of rope is neglected. calculate tension in rope, if accelerate up rope at 0.40 m/s^2

T = m(g+a)
T = 70.0(9.8+.4)
= 714 N


slides downward acceleration of .40
T = m(g-a)
t = 70.0(9.8-.4)
= 685 N

looks good?
 
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Looks fine to me.
 
bigman8424 said:
a 70.0 kb man climbs vertical rope attached to ceiling. weight of rope is neglected. calculate tension in rope, if accelerate up rope at 0.40 m/s^2

T = m(g+a)
T = 70.0(9.8+.4)
= 714 N


slides downward acceleration of .40
T = m(g-a)
t = 70.0(9.8-.4)
= 685 N

looks good?
Might just be me, but if he goes up at 0.4 then g is -9.8 because it is acting in the opposite direction. If you think about it in the direction as g is 9.8 then is acceleration is going to be -0.4.

So the second one looks good to me. :smile:

The Bob (2004 ©)
 
The Bob said:
Might just be me, but if he goes up at 0.4 then g is -9.8 because it is acting in the opposite direction. If you think about it in the direction as g is 9.8 then is acceleration is going to be -0.4.

So the second one looks good to me. :smile:

The Bob (2004 ©)
As he goes up he pulls down on the rope.
 
whozum said:
As he goes up he pulls down on the rope.
I see. :smile:

Cheers. :biggrin:

The Bob (2004 ©)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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