Easy problem dealing with tension and mass of an object.

[epicwinning97]

Homework Statement

The box on the frictionless ramp is held at rest by the tension force. The mass of the box is 20kg. What is the value of the tension force?

Homework Equations

sine=opp/hyp cosine=adj/hyp F=ma

The Attempt at a Solution

Did 20*9.8 to get the force of gravity on the object (196N). Then I took the cosine of 30 and got .866. I then divided 196 by this and got 226N for the hypotenuse. Is this correct? Thanks!
DIAGRAM:http://img838.imageshack.us/img838/6927/diagramu.png

EDIT: So, the Newtons needed to hold it when the slope is 0 would be 196. I also found the Newtons for it at 89 degrees, which was about 11,000. So, according to my math, the tension force is 226N. Now I just need to find the normal force. Any ideas?

 

[PeterO]

Homework Statement

The box on the frictionless ramp is held at rest by the tension force. The mass of the box is 20kg. What is the value of the tension force?

Homework Equations

sine=opp/hyp cosine=adj/hyp F=ma

The Attempt at a Solution

Did 20*9.8 to get the force of gravity on the object (196N). Then I took the cosine of 30 and got .866. I then divided 196 by this and got 226N for the hypotenuse. Is this correct? Thanks!
DIAGRAM:http://img838.imageshack.us/img838/6927/diagramu.png

Each of those calculations is correct, but now you have to relate them to the question.

EDIT: if the angle of the slope was 0^o what value would you get from your calculations, and what tension would be needed to keep the mass in place?

 

[BetoG93]

Mmmm... I did the same problem and got 98 N for tension. Remember that the direction of normal force is perpendicular to surface, and it isn't antiparallel to the force of gravity. You have to find the components of the force of gravity, too.
Add all components and set it equal to zero, since it is at rest.

 

[BetoG93]

The normal force is equal to a component of the force of gravity. (Try to find out which one

 

[asteriatic]

I would first commend you for using the appropriate equations and attempting to solve the problem. However, I do have a few suggestions for improvement.

Firstly, it would be helpful to label your diagram with the appropriate variables (e.g. F for force, m for mass, θ for angle) to clearly show what each value represents. This will make it easier to follow your calculations.

Secondly, your approach to finding the tension force is correct, but your calculations are not entirely accurate. The tension force should be equal to the force of gravity on the object, which is 196N, as you correctly calculated. However, your calculation for the hypotenuse is incorrect. The hypotenuse should be equal to the weight of the object (196N) divided by the cosine of the angle (0.866), which gives a value of 226.23N. This means that the tension force is also 226.23N, not just 226N.

As for finding the normal force, you can use the equation F = ma to calculate it. Since the object is at rest, the net force on it must be zero. This means that the normal force must be equal in magnitude to the force of gravity (196N), but in the opposite direction. So the normal force is also 196N.

In conclusion, the tension force is 226.23N and the normal force is 196N. I hope this helps and keep up the good work in solving scientific problems!