What is the tension force of the rope in this physics problem?

[F|reWa||]

I am totally stuck on these two and I would like to know how to do this problem:

1. A 100 pound weight is resting on a 30 degree ramp with a coefficient of friction µ = 0.35 and is restrained by a rope. What is the tension force of the rope?

Sin 30 degrees = 0.5
Cos 30 degrees = 0.866
Tan 30 degrees = 0.577

2. A jet plane is climbing at a constant airspeed in no-wind conditions. The plane takes off from sea level. The plane is directly over a point on the ground that is 4 statute miles (21,120 ft) from the takeoff point and the altimeter reads 15,840 ft. Find the tangent of the climb angle and the distance that it has flown through the air.

Thanks :)

-AML

 

[russ_watters]

For problem 1, break the gravitational force into two components - one parallel to the plane and one perpendecular. Friction force is calculated from the perpendicular component. Subtract the friction force from the parallel component of the weight.

For problem 2, draw a triangle and solve it.

 

[FZ+]

Also, it's generally better in such problems to use the exact values if possible, and round up later. eg. sin 30 = 0.5 , cos 30 = 0.5 * [squ]3, tan 30 = 1/([squ]3)

However, the question as you gave it is not entirely correct. The coefficient of friction gives the limiting static friction of the two surfaces. You cannot use F = [mu] R unless you assume friction is at limiting. But that's a minor point. It probably doesn't matter.