CP CALC ?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) = (3.0 m/s2)t + (0.20 m/s3)t2. When t = 4.0 s, what is the reading on the bathroom scale?

Solution 77P Step 1: Your mass is 64 kg. The elevator starts accelerating upwards. The velocity as a function of time is given as, 2 v(t) = 3t + 0.20 t ----------------(1) As we know that, acceleration is the time derivative of velocity, so let’s find it. dv d 2 a = dt = dt(3t + 0.20 t ) = 3 + (0.20 × 2) t = 3 + 0.40t St time t = 4 s, the acceleration will be, a = 3 + 0.40 × 4 = 4.6 m/s .2 Step 2: The weight is how much normal reaction an object is getting. To visualize this let’s see the diagram. Here in this figure, a block of mass m is getting the normal reaction of mg. So, it’s weight is mg. Now think of an object in an elevator which is accelerating upwards with an acceleration “a”. The diagram is shown below. The equation for which can be written as, N mg = ma N = mg + ma = m(g + a)------------------(2)