Finding tension of a rope pulling a crate

In summary, the conversation discusses finding the tension of a rope in a physics problem. By substituting equations and using algebra, the tension is calculated to be approximately 108N, which is less than the weight of the crate being pulled.
  • #1
Timebomb3750
59
0
Did this problem out, but answer doesn't look right.

Homework Statement


Find the tension of the rope.

M=37.7kg
Coefficient of kinetic friction=.244
Rope is at an angle of 22.2° above the horizontal
Pulled at constant speed, meaning a=0

Homework Equations


I figured that...
ƩFx=Tcos∅-μkN=0
ƩFy=N-mg-Tsin∅=0

So, N=mg+Tsin∅

Then I did a simple substitution with the N equation...

Tcos∅-μkmg+Tsin∅=0

When I got T by itself, I got...

T=(μkmg/cos∅+sin∅)

The Attempt at a Solution



Then I just plugged the given numbers in, and I got T=69N (Approximately)

Am I correct? Because I figured the tension of the rope has to be greater than the mg of the crate.
 
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  • #2
ƩFy=N-mg-Tsin∅=0

Replace -Tsinangle by +Tsinangle
 
  • #3
grzz said:
ƩFy=N-mg-Tsin∅=0

Replace -Tsinangle by +Tsinangle

Okay, so that means that my final equation for T changes to...

T=(μk*mg/cos∅-sin∅)

I get an answer of about 164.5 N. It's higher, but is that right. I'm still wondering if T is supposed to be greater than the mg of the crate. If this is correct, then why did I have to change the -Tsin∅, to a positive Tsin∅?
 
  • #4
bump.
 
  • #5
When you sum forces in the y direction, N acts up (+), mg acts down (-), and T sin theta acts up (+). That is why grzz corected the signage for Tsin theta.

Beyond that, your algebra is incorrect. There should be a uk in front of the Tsin theta term (note that a(b + c) = ab + ac).

Why do you feel T has to be greater than mg? Consider pulling a heavy crate on a near frictionless surface. The pulling force is much less than mg.
 
  • #6
PhanthomJay said:
When you sum forces in the y direction, N acts up (+), mg acts down (-), and T sin theta acts up (+). That is why grzz corected the signage for Tsin theta.

Beyond that, your algebra is incorrect. There should be a uk in front of the Tsin theta term (note that a(b + c) = ab + ac).

Why do you feel T has to be greater than mg? Consider pulling a heavy crate on a near frictionless surface. The pulling force is much less than mg.

Ah, I see now.

Didn't catch the algebra error. Thanks for that.

Meh. I don't know what I was thinking earlier. Was doing this problem early in the morning.

Okay, so now that I corrected my errors, I get a tension of approximately 108 N.
 
  • #7
looks good!
 

1. What is tension and why is it important to find the tension of a rope pulling a crate?

Tension is a force that is created when an object is pulled or stretched. In the case of a rope pulling a crate, tension is the force that the rope exerts on the crate in order to move it. It is important to find the tension in order to ensure that the crate can be moved safely and efficiently without causing any damage.

2. How do you calculate the tension of a rope pulling a crate?

The tension can be calculated using the formula T = F * sinθ, where T is the tension, F is the force being applied to the rope, and θ is the angle between the rope and the direction of the force. This formula takes into account the angle at which the force is being applied, as it can affect the amount of tension in the rope.

3. What factors can affect the tension of a rope pulling a crate?

The tension of a rope pulling a crate can be affected by a number of factors, including the weight of the crate, the strength of the rope, and the angle at which the rope is being pulled. Other factors such as friction and the condition of the rope can also play a role in the amount of tension exerted.

4. How does the tension of the rope change as the crate is being pulled?

The tension of the rope will increase as the crate is being pulled. This is because as the crate moves, it creates a resistance force in the opposite direction of the pull, causing an increase in tension on the rope. The tension will continue to increase until the crate reaches a constant velocity, at which point the tension will remain constant.

5. What safety precautions should be taken when determining the tension of a rope pulling a crate?

When determining the tension of a rope pulling a crate, it is important to ensure that the crate and all equipment (such as the rope and pulleys) are in good condition and able to withstand the calculated tension. It is also important to wear appropriate safety gear and to have a clear understanding of the forces involved in order to prevent any accidents or injuries.

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