Help with Kinetic Energy and Time

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SUMMARY

The discussion focuses on calculating the shortest time for a pickup truck to accelerate uniformly to 32.0 m/s without causing a toolbox to slide out due to friction. The coefficients of static and kinetic friction are given as 0.700 and 0.305, respectively. By applying Newton's second law, the maximum static frictional force can be determined, which allows for the calculation of the maximum acceleration. Subsequently, this acceleration is used to find the time required to reach the target speed of 32.0 m/s.

PREREQUISITES
  • Understanding of Newton's second law
  • Knowledge of static and kinetic friction coefficients
  • Ability to perform basic kinematic equations
  • Familiarity with force diagrams
NEXT STEPS
  • Calculate maximum static friction force using the formula: F_friction = μ_static * N
  • Determine the maximum allowable acceleration using Newton's second law: F = m * a
  • Use kinematic equations to find time: t = (v_f - v_i) / a
  • Explore real-world applications of friction in vehicle dynamics
USEFUL FOR

Physics students, automotive engineers, and anyone interested in understanding the dynamics of friction and acceleration in vehicles.

kgianqu2
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A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is set moving. The coefficients of kinetic and static friction between the box and the bed of the truck are 0.305 and 0.700, respectively.

Starting from rest, what is the shortest time this truck could accelerate uniformly to 32.0 ( 71.6) without causing the box to slide. (Hint: First use Newton’s second law to find the maximum acceleration that static friction can give the box, and then solve for the time required to reach 32.0 .)

I am not sure what formulas to use or how to solve the problem, please help. Thanks.
 
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Draw a force diagram of the box while the truck is accelerating, but when the box isn't sliding. Then just balance forces.
 

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