Question

You build a 2.0-kg mound of mashed potatoes on a kitchen scale (which is a spring scale). You then use a large spoon to press on the top of the mound at a constant force of 3.0 N. While you are doing this, the scale reading increases by 5.0%. (a) What is the acceleration of the center of mass of the potatoes? (b) Describe what happens to the shape of the mound and the scale reading as time goes by.

Answer 1

Answer:

a= -1.01m/s^2

Explanation:

A) We define all the variables that are given,

In this way

Acceleration = a

$m = 2.0Kg$

$F = 3.0N$

We obtain the Normal assuming 5% of the potato reading scale, so

$N = (2 + 2 * 5\%) * 9.8$

$N = 20.58N$

We add forces to reach equilibrium, and you get

$N-F-mg = ma$

** The notation of the symbols is done according to the notation of the graph

So,

$a = \frac {N-F-mg} {m}$

$a = \frac {20.58-3-2 * 9.8} {2}$

$a = -1.01m / s ^ 2$

B) When making pressure it is understood that the shape takes the perpendicular direction of the direction of the force that is performed. If the pressure remains constant, the scale will also increase in its measurement.

Answer 2

Answer:

a) $a=1m/s^2$ downwards

b) The mound will be reduced in height (the acceleration is downwards) and will begin to grow sideways. The reading will remain the same until the spoon reaches the scale surface.

Explanation:

On the mound, the forces acting before the spoon are:

N1 - m*g = 0   Where N1 is equivalent to the reading of the scale.

N1 = 2*10 = 20N

After the spoon starts pressing, this value increases by 5%:

N2 = 20*105% = 21N  So, at this point the forces on the moud are:

N2 - m*g - F = m*a   Solving for a:

a = -1m/s^2   This result tells us that the center of mass of the potatoes is moving downwards. Since it cannot move because of the scale, it has no other option than to grow sideways as it is pushed.