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

[Jtappan]

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.

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.

 

[hage567]

You shouldn't need the mass, since it will be common to each term and you will be able to cancel it out.