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.

 

[ogb p]

Assuming that the mass is not given, we cannot calculate the speed at any of the positions. In order to calculate the speed at each position, we need to know the total energy at each position, which in turn requires us to know the mass of the cart. Additionally, the given information only tells us the initial velocity at position 4 and does not provide any information on how the cart moves from position 4 to the other positions. Therefore, without more information, it is not possible to accurately calculate the speed at positions 1, 2, and 3.