Question

You are standing on a bathroom scale in an elevator in a tall building. Your mass is

64 kg. The elevator starts from rest and travels upward with a speed that varies with time according to v(t)=(3.0m/s2)t+(0.20m/s3)t2.

When
t=4.0s, what is the reading of the bathroom scale?

Answer 1

Answer:

94 kg or 921.6 N

Explanation:

The velocity function is $v(t) = 3t + 0.2t^2$. The acceleration function, a(t), is the time derivative of the velocity function.

$a(t) = \dfrac{d}{dt}v(t) = 3 + 0.4t$

At $t=4$,

$a(4) = 3 + 0.4\times4 = 3+1.6 =4.6\text{ m/s}{}^2$

Because the elevator is going upwards, the net acceleration, $a_N = g + a(4)$ where g us acceleration of gravity.

$a_N = 9.8 + 4.6 = 14.4\text{ m/s}{}^2$

The resultant weight is

$W =m a_N =64\times14.4=921.6 \text{ N}$

Since the bathroom scale is graduated in kg, it's reading is

$m =\dfrac{W}{g}=\dfrac{921.6}{9.8}=94\text{ kg}$

Answer 2

Using the concept of Newton's second law, as the elevator starts from rest and travels upward, the scale shows a value of 94.04 kg

Newton's Second Law of Motion

Acceleration is the time derivative of velocity. Therefore acceleration can be given by;

$a=a(t)=\frac{dv(t)}{dt} = \frac{d}{dt} (3t+0.2t^2) = 3+0.4t$

When t = 3s;

$a= 3+(0.4\times 4)=4.6\,m/s^2$

As the elevator is moving upward the net force on the weighing scale is given using Newton's second law of motion;

$F_{net}=m(a+g) =(64\,kg)\times (9.8\,m/s^2 +4.6\,m/s^2)=921.6\,N$

A weighing scale is usually caliberated to show the value in kilograms.

Therefore the weighing scale will show the reading;

$m=\frac{F_{net}}{g} =\frac{921.6\,N}{9.8\,m/s^2}= 94.04\,kg$

Learn more about Newton's second law of motion here:

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