Laws of Motion, vertical acceleration question.

[Bucky]

"In a lift accelerated upwards at a certain rate, a spring balance indicates a weight to have a mass of 10kg. When the lift is accelerated downwards at twice the upward rate, the mass appears to be 7kg. Find the actual mass and the upward acceleration of the lift."

In short, I am stuck. I think this question involves simultaneus equations, but i can't get a set of equations that make sense. I've looked at the textbooks I have but they all concern themselves with the resistance forces or tensions in the strings.

 

[nishant]

try to put in pseudo forces on the block

 

[OlderDan]

"In a lift accelerated upwards at a certain rate, a spring balance indicates a weight to have a mass of 10kg. When the lift is accelerated downwards at twice the upward rate, the mass appears to be 7kg. Find the actual mass and the upward acceleration of the lift."

In short, I am stuck. I think this question involves simultaneus equations, but i can't get a set of equations that make sense. I've looked at the textbooks I have but they all concern themselves with the resistance forces or tensions in the strings.

A spring balance really measures force, not mass. It is marked with mass units assuming you will be using it in an inertial (non-accelerating) frame of reference. When it reads 10kg that really means the force it is measuring is 10kg(g) and when it reads 7kg, that means the force is 7kg(g)

Call the upward acceleration a and the downward acceleration -2a, taking positive upward in all cases.

F = ma = Force of spring balance (up) acting on m - weight
F = -2ma = Force of spring balance (down) acting on m - weight

Replace the words with the correct quantities and you are on your way.

 

[Bucky]

thanks for the help but I am still not sure what I am doing here...

f=ma
f=(10)a
f=10a (1)


f=ma
f=(7)(-2a)
f=-14a (2)

that seems wrong.

 

[HallsofIvy]

You say "thanks for the help" but you don't seem to understand what was said! OlderDan just told you that the "10kg" and "7kg" reading on the scale is NOT mass- it is force- you should be substituting it for f, not m. m is what you are asked to find.
Also you don't have "g" in your formulas- the weight of mass m is mg. When the scale reads "10 kg" it is actually measuring a force of 10g Newtons.

f= ma so, in order to accelerate the mass m upwards at acceleration a, the elevator must apply force ma to the mass, through the scale. The scale is reading the weight of the mass, mg, plus the force ma: ma+ mg= m(a+g)= 10g
When the elevator is accelerating downwards, with acceleration -2a, and so the scale is reading -2ma+ mg= 7g Solve those two equations for m and a (g= 9.81 m/s², of course).