A person sitting inside an elevator performs | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The height of the elevator is given by $y = 8 + 8 \sin(\frac{2 \pi t}{T})$.Taking the second derivative with respect to time $t$,we find the accel

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) The height of the elevator is given by $y = 8 + 8 \sin(\frac{2 \pi t}{T})$.Taking the second derivative with respect to time $t$,we find the acceleration of the elevator: $a = \frac{d^2y}{dt^2} = -8(\frac{2 \pi}{T})^2 \sin(\frac{2 \pi t}{T})$.The apparent weight of the object is $W' = m(g + a)$.The variation in weight is $\Delta W = m \cdot |a|$.The maximum acceleration is $a_{\max} = A \omega^2$,where $A = 8 \ m$ and $\omega = \frac{2 \pi}{T} = \frac{2 \pi}{40 \pi} = 0.05 \ rad/s$.Thus,$a_{\max} = 8 	imes (0.05)^2 = 8 	imes 0.0025 = 0.02 \ m/s^2$.The variation in weight is $\Delta W = m \cdot a_{\max} = 50 	imes 0.02 = 1 \ N$.However,considering the full range of oscillation (from $+a_{\max}$ to $-a_{\max}$),the total variation is $2 	imes m 	imes a_{\max} = 2 	imes 50 	imes 0.02 = 2 \ N$.

Similar Questions

$A$ coin is dropped in a lift. It takes time $t_1$ to reach the floor when the lift is stationary. It takes time $t_2$ when the lift is moving up with constant acceleration $a$. Then:

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring balance reads $49 \,N$, when the lift is stationary. If the lift moves downward with an acceleration of $5 \,m/s^2$, the reading of the spring balance will be $(g = 9.8 \,m/s^2)$. (in $\,N$)

An elevator car,whose floor-to-ceiling distance is $2.7 \, m$,starts ascending with a constant acceleration of $1.2 \, m/s^2$. $2 \, s$ after the start,a bolt begins falling from the ceiling of the car. The free-fall time of the bolt is ......... $s$.

$A$ man of mass $75\, kg$ is standing in an elevator which is moving with an acceleration of $5\, m/s^2$ in the upward direction. The apparent weight of the man will be ........... $N$ $(g = 10\, m/s^2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module