Finding acceleration of truck from a hung mass on the ceiling of it.

AI Thread Summary
To find the acceleration of a truck with a mass suspended from its ceiling, the problem involves analyzing forces acting on the mass. The mass creates a tension in the string that can be broken down into horizontal and vertical components, leading to equations based on F=ma. The angle of 22° indicates a relationship between the acceleration of the truck and gravitational force, which can be expressed using trigonometric functions. The calculations provided yield conflicting results, suggesting a need for a clearer approach to resolving the components. Understanding the triangle formed by the forces is crucial for accurately determining the truck's acceleration.
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Homework Statement



A mass M = 74.0 kg is suspended by a massless string from the ceiling of a van which is moving with constant acceleration a, as shown in the figure.
1262751-1315-setDynamics_no_friction-prob5--prob24a.gif


If the string makes an angle theta = 22° with respect to the vertical, what is the acceleration a of the van?

Homework Equations



All I can think of is F=ma

The Attempt at a Solution



I found the force of the x component and the y component (-27.72N and 793.8N resp.) I tried 27.72=74.0a=.375m/s^2 and 793.8=74a=10.727m/s^2. I tried adding/substracting tthe answers. I don't know what to try anymore.
 
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tan-1(a/g)=22°

Look it like a triangle. the angle is 22 theta, the vertical component is g, the horizontal is a.
 
Thank-you so much!
 
No-Problem! XD
 

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