M1 motion on a plane question

A boat on a trailer is held in equilibrium on a slipway inclined at 20° to the horizontal, by a cable inclined at θ to the slope. The combined mass of the boat and trailer is 1250 kg. The cable may break if the tension exceeds 7000 N. Find the maximum value of θ.

So the force going down the slope because of gravity is 1250g/sin20 which is 35816.6039

Then what do I do to find θ?

Reply 1

ghostwalker

Original post by 000alex

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The weight acting down the slope is 1250gsin20, not 1250g/sin20

This needs to equal the component of the tension in the cable going up the slope, which is 7000sin theta.

Reply 2

000alex

Original post by ghostwalker

The weight acting down the slope is 1250gsin20, not 1250g/sin20

This needs to equal the component of the tension in the cable going up the slope, which is 7000sin theta.

Why isn't it 1250g/sin20

Don't you use sinθ=o/h and o=1250g ???

Also why isn't it 7000cosθ ?

(edited 10 years ago)

Reply 3

ghostwalker

Original post by 000alex

Why isn't it 1250g/sin20

Don't you use sinθ=o/h and o=1250g ???

Also why isn't it 7000cosθ ?

Draw a diagram if you haven't already. You're resolving the weight (1250g) in the direction of the slope. The force being resolved always forms the hypotenuse of the triangle.
h=1250g.