A body of mass 80kg stands on a weighing machine in a lift. Determine the reading on the weighing machine when the lift moves;(a)downwards at constant velocity of 2.0m/s (b)downwards with an acceleration of 3m/s (c)upward with acceleration of 3m/s
mg
m(g-3)
m (g+3)
To determine the reading on the weighing machine in different scenarios, we need to consider the forces acting on the body and apply Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m*a).
Let's break down each scenario and calculate the readings on the weighing machine:
(a) When the lift moves downward at a constant velocity of 2.0 m/s:
In this scenario, the lift is moving at a constant velocity, which means there is no net force acting on the body. The force due to gravity (weight) and the normal force from the weighing machine balance each other.
Since the net force is zero, the reading on the weighing machine will be equal to the weight of the body.
Weight = mass * acceleration due to gravity
Weight = 80 kg * 9.8 m/s^2
Weight = 784 N
Therefore, the reading on the weighing machine when the lift moves downward at a constant velocity of 2.0 m/s will be 784 N.
(b) When the lift moves downward with an acceleration of 3 m/s^2:
In this scenario, the lift moves downward, and there is an additional downward acceleration of 3 m/s^2 acting on the body. We need to consider both the force due to gravity and the additional downward force caused by the acceleration.
Net Force = Force due to gravity - Additional downward force
Net Force = m * g - m * a (where m is the mass, g is the acceleration due to gravity, and a is the additional downward acceleration)
Net Force = 80 kg * 9.8 m/s^2 - 80 kg * 3 m/s^2
Net Force = 784 N - 240 N
Net Force = 544 N
The reading on the weighing machine will be equal to the net force acting on the body, which is 544 N.
(c) When the lift moves upward with an acceleration of 3 m/s^2:
In this scenario, the lift moves upward, and there is an additional upward acceleration of 3 m/s^2 acting on the body. We need to consider both the force due to gravity and the additional upward force caused by the acceleration.
Net Force = Force due to gravity + Additional upward force
Net Force = m * g + m * a (where m is the mass, g is the acceleration due to gravity, and a is the additional upward acceleration)
Net Force = 80 kg * 9.8 m/s^2 + 80 kg * 3 m/s^2
Net Force = 784 N + 240 N
Net Force = 1024 N
The reading on the weighing machine will be equal to the net force acting on the body, which is 1024 N.
Remember, the reading on the weighing machine represents the force exerted by the body on the weighing machine, which is equal to the weight of the body in the absence of other forces.