A man whose mass is 80kg stands on a sprin
g weighing machine inside an elevator. What is the reading of the weighing machine when the elevator starts to ascend with an acceleration of 2
Answers
Answer
To find the reading on the weighing machine, we need to consider the forces acting on the man when the elevator starts to ascend with an acceleration of 2 m/s^2.
The two main forces acting on the man are his weight (due to gravity) and the normal force exerted by the weighing machine.
1. Weight (gravity force):
The weight of an object is given by the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the man is 80 kg. Therefore, his weight would be:
W = 80 kg * 9.8 m/s^2 = 784 N.
2. Normal force (weighing machine):
The normal force is the force exerted by a surface to support the weight of an object resting on it.
In this case, when the elevator starts to ascend, there is an additional upward acceleration acting on the man. This means that the weighing machine needs to exert an additional force to support him.
The normal force can be calculated using the formula N = W + ma, where N is the normal force, W is the weight, m is the mass, and a is the acceleration.
In this case, the additional acceleration is 2 m/s^2. Therefore, the normal force would be:
N = 784 N + (80 kg * 2 m/s^2) = 784 N + 160 N = 944 N.
So, the reading on the weighing machine when the elevator starts to ascend with an acceleration of 2 m/s^2 would be 944 Newtons.