A spring is suspended on the ceiling of a truck, find acceleration?

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SUMMARY

The problem involves a massless spring with a spring constant of 500 N/m, suspended from a truck's ceiling, which experiences horizontal acceleration. A 1.1 kg toy causes the spring to extend by 5.0 cm when the truck accelerates. To determine the truck's acceleration, one must analyze the forces acting on the spring and the toy, considering the spring force and the net force equations. The spring's angle with respect to the vertical increases as the truck accelerates, indicating a relationship between the horizontal acceleration and the vertical extension of the spring.

PREREQUISITES
  • Understanding of Hooke's Law (Fk = -kx)
  • Basic knowledge of Newton's second law (Fnet = ma)
  • Ability to draw and interpret free body diagrams
  • Concept of forces acting in different directions
NEXT STEPS
  • Calculate the net force acting on the toy using Fnet = ma
  • Explore the relationship between the spring's angle and the truck's acceleration
  • Learn about vector components in force analysis
  • Investigate the effects of different spring constants on acceleration calculations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and force analysis, as well as educators looking for practical examples of applying Newton's laws in real-world scenarios.

greenglasses
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Homework Statement



A massless spring with a spring constant k = 500 N/m is suspended from a hook on the ceiling of a cargo truck moving in a straight line (horizontally) on the highway. A child reaches over from her seat and suspends a 1.1 kg toy on the free end of the spring. The child notices that the spring is now 5.0 cm longer than when it was hanging freely. Find the acceleration for the truck.

Homework Equations



Fk = -kx
Fnet = ma

The Attempt at a Solution



I honestly have no clue what to do since the spring force is in the vertical direction but the truck is accelerating horizontally. Would appreciate any pointers in the right direction.
 
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greenglasses said:

The Attempt at a Solution



I honestly have no clue what to do since the spring force is in the vertical direction but the truck is accelerating horizontally. Would appreciate any pointers in the right direction.

Draw a free body diagram. The weighted spring will not remain vertical when the truck is accelerating. The greater the acceleration, the greater the spring extends and the greater the springs angle wrt vertical becomes.
 

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