What is the angle and the tension??? (I'm really confused)?

Question

A 0.500-kg object is suspended from the ceiling of an accelerating boxcar. If a = 3.00 m/s2, find (a) the angle that the string makes with the vertical and (b) the tension in the string

Answer 1

Draw an force diagram.

If the train car is acceleration forward at 3 m/s^2 then so must the suspended object. There must be some force acting on the object in the direction of the trian's acceleration to keep it from flying to the back of the train.
Also, if not for the rope, the object would fall to the ground...there must be some upward force acting on the object to balance its weight.

When you draw the diagram it should should have perpendicular forces acting on the block...one pointing straight down (the object's weight due to gravity), another pointing straight up (the balancing force provided by the rope), and another pointing perfectly horizontal. Where are these forces coming from? The rope of course. The force of tension in the rope must provide the forward accelerating force to the the object and the balancing force for the balancing force to counter-act gravity. The angle between these forces should be the angle of the rope and the magnitude of these forces added together should equal the tension in the rope.

You know the object's mass so you should be able to find its weight,
W = mg
and the net horizontal force to cause a 3 m/s^2 acceleratino
F = ma

Answer 2

Draw a triangle.

The vertical is the weight of the .5 kg mass (Multiply times 9.8 netwtons/kg)

The horizontal is the force of acceleration F=Ma...
F (newtons) = .5 * 3.00 m/s2

Now you have the vertical and horizontal componante, use pythagorus to find the length of the hypotenuse, and that is the tension.

Use the law of Cosine, and get the angle.

Answer 3

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