Calculate tension if acceleration given

In summary, the tension in the rope is calculated to be 714 N when the man is accelerating upwards at 0.40 m/s^2 and 685 N when he is sliding downwards at the same acceleration. The opposite direction of gravity must be taken into account when calculating the tension in the rope. The man also exerts a downward force on the rope as he climbs up.
  • #1
bigman8424
25
0
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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  • #2
Looks fine to me.
 
  • #3
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 ©)
 
  • #4
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.
 
  • #5
whozum said:
As he goes up he pulls down on the rope.
I see. :smile:

Cheers. :biggrin:

The Bob (2004 ©)
 

1. How do I calculate tension if acceleration is given?

To calculate tension if acceleration is given, you can use the formula T = ma, where T is tension, m is mass, and a is acceleration. Simply plug in the known values and solve for tension.

2. Can I use the same formula to calculate tension in different situations?

Yes, the formula T = ma can be used to calculate tension in various situations as long as you have the values for mass and acceleration. However, in some cases, you may need to consider other factors such as friction or gravity.

3. What units should I use for mass and acceleration when calculating tension?

For consistency, it is best to use the standard units of measurement for mass (kilograms) and acceleration (meters per second squared) when calculating tension. This will ensure accurate results and make it easier to compare with other calculations.

4. Can tension be negative if acceleration is negative?

Yes, tension can be negative if acceleration is negative. This simply means that the force is acting in the opposite direction of the tension. However, in most cases, tension is considered to be a positive value as it represents the force pulling on an object.

5. Is it possible to calculate tension without knowing the acceleration?

No, it is not possible to calculate tension without knowing the acceleration. This is because the formula T = ma requires both the mass and acceleration values to solve for tension. If you do not know the acceleration, you will need to gather more information or use a different formula to calculate tension.

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