A lift is going up. The total mass of the lift and the passenger is 1000 kg The variation in th

step 1 Hi, student, welcome to the solution of problem number 332. A lift is going up. Suppose this is

A lift is going up. The total mass of the lift and the...

A lift is going up. The total mass of the lift and the passenger is $1000 \mathrm{~kg}$ The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $\mathrm{t}=10.5 \mathrm{sec}$ will be (A) $8000 \mathrm{~N}$ (B) Zero (C) $12000 \mathrm{~N}$ (D) $17400 \mathrm{~N}$

A lift is going up. The total mass of the lift and the passenger is $1000 \mathrm{~kg}$ The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at $\mathrm{t}=10.5 \mathrm{sec}$ will be
(A) $8000 \mathrm{~N}$
(B) Zero
(C) $12000 \mathrm{~N}$
(D) $17400 \mathrm{~N}$

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Key Concepts

Tension in an Accelerating System

In a system where an object is accelerating, the tension in the supporting rope must counteract both the gravitational force and the force required for acceleration. This is expressed by the equation T = m(g + a) for upward acceleration, illustrating how the concepts of mass, gravity, and acceleration interact to determine the net tension force.

Acceleration from a Velocity-Time Graph

Acceleration is the derivative of velocity with respect to time. A velocity-time graph’s slope at any point gives the instantaneous acceleration of the moving object, which is crucial for determining the net force acting on a system, such as an elevator at a particular time.

Newton's Second Law

Newton’s Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is key to understanding how forces produce acceleration in any system, including an elevator in motion.

Gravitational Force

Gravitational force is the pull exerted by the Earth on any mass, calculated as F = mg, where m is the mass and g is the acceleration due to gravity. In problems involving lifts, this force represents the constant downward pull that must be overcome by the upward tension force.

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