Calculating Speed of Cart at Positions 1, 2, and 3

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SUMMARY

The discussion focuses on calculating the speed of a cart at positions 1, 2, and 3, starting from position 4 with an initial velocity of 13 m/s to the left. The total energy conservation principle is applied, where the total energy (E_tot) remains constant across all positions, combining kinetic energy (E_kin) and potential energy (E_pot). The gravitational constant (g = 9.81 m/s²) is used to determine potential energy, while the mass of the cart is not required for calculations as it cancels out in the equations. The key takeaway is that the speeds at each position can be derived without knowing the mass of the cart.

PREREQUISITES
  • Understanding of kinetic energy (E_kin = 1/2 * m * v²)
  • Familiarity with potential energy (E_pot = m * g * h)
  • Knowledge of the conservation of energy principle
  • Basic physics concepts related to motion and forces
NEXT STEPS
  • Study the principles of energy conservation in physics
  • Learn how to apply the conservation of energy to solve motion problems
  • Explore examples of calculating speed in vertical motion scenarios
  • Investigate the effects of friction on energy conservation in real-world applications
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Homework Statement


A cart starts from position 4 in the figure below with a velocity of 13 m/s to the left. Find the speed with which the cart reaches positions 1, 2, and 3. Neglect friction.
fig-030.gif


speed at position 1 ___ m/s
speed at position 2 ___ m/s
speed at position 3 ___ m/s

Homework Equations



E_tot1 = E_tot2 = E_tot3 = E_tot4

The total energy is kinetic energy plus potential energy
E_tot = E_kin + E_pot

E_pot = m * g * h
with m the mass of the cart, g the gravitational constant of Earth (g=9.81m/s^2) and h the height.

E_kin = 1/2 * m * v^2


The Attempt at a Solution



I attempted to do this problem and I cannot figure out how to solve for any of them if I am not given the mass of the cart.
 
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You shouldn't need the mass, since it will be common to each term and you will be able to cancel it out.
 

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