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

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SUMMARY

The discussion focuses on calculating the acceleration of a van based on a suspended mass and the angle of the string. Given a mass (M) of 74.0 kg and an angle (theta) of 22° with respect to the vertical, the acceleration (a) of the van can be determined using the components of forces. The x-component of the force is calculated as -27.72 N, while the y-component is 793.8 N. The correct approach involves using the relationship between the angle and the acceleration, leading to the equation tan(22°) = a/g, where g is the acceleration due to gravity.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Basic trigonometry, specifically tangent functions
  • Knowledge of gravitational acceleration (g = 9.81 m/s²)
  • Ability to resolve forces into components
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  • Explore the application of trigonometric functions in physics problems
  • Review examples of dynamics involving suspended masses
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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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