A potato salesman has set up a bootleg potato shop inside an elevator. He sells his potatoes by placing them on a spring scale suspended from the ceiling (like the ones at the grocery store). When the elevator is accelerating upward, is the weight of the potatoes themselves the same, more, or less than they do when the elevator is at rest? How does this compare to the reading on the scale? Think carefully and clearly explain your answer.
The weight is m g, does not change as long as g = 9.81 m/s^2 more or less.
HOWEVER the scale measures the force exerted on the sack of potatoes by the spring in the scale.
When stationary, a = 0, the force on the spring = m g
When accelerating at "a" up we have
Spring force up - m g = m a
so
Spring force = m g + m a
When the elevator is accelerating upward, the weight of the potatoes themselves does not change. The weight of an object is the force with which it is pulled toward the center of the Earth due to gravity. This force remains constant unless the mass of the object or the acceleration due to gravity changes.
The scale, on the other hand, measures the force acting on it, which in this case is the force exerted by the potatoes. When the elevator is at rest, the scale accurately measures the weight of the potatoes because there are no additional forces acting on them apart from gravity.
However, when the elevator is accelerating upward, an additional force acts on the potatoes - the force of acceleration. This force pushes the potatoes upward and reduces the force with which they are pulled towards the center of the Earth. As a result, the reading on the scale will be less than their actual weight.
To summarize, the weight of the potatoes themselves remains the same whether the elevator is at rest or accelerating upward. However, the reading on the scale will be less than their actual weight when the elevator is accelerating upwards due to the additional force of acceleration.
When the elevator is accelerating upward, the weight of the potatoes themselves remains the same. This is because weight is a measurement of the force of gravity acting on an object, and the force of gravity on the potatoes doesn't change regardless of the elevator's movement. The weight of the potatoes is determined by the mass of the potatoes and the gravitational acceleration.
However, the reading on the spring scale may be different when the elevator is accelerating upward. This is because the scale measures the force exerted on it, which is different from the weight.
When the elevator is at rest, the scale reads the weight of the potatoes correctly since there is no additional force acting on the potatoes. The force exerted by the potatoes is equal to their weight, and this force is balanced by the upward force exerted by the scale.
When the elevator is accelerating upward, there is an additional force acting on the potatoes known as the "inertial force" or "pseudo-force." This inertial force is generated due to the acceleration of the elevator and is directed opposite to the direction of acceleration. The scale measures the sum of the weight of the potatoes and the inertial force. As a result, the reading on the scale will be more than the actual weight of the potatoes.
To determine the actual weight of the potatoes when the elevator is accelerating upward, we need to subtract the inertial force from the reading on the scale. The inertial force can be calculated using Newton's second law (F = ma), where 'm' is the mass of the potatoes and 'a' is the acceleration of the elevator. Once we have determined the inertial force, we can subtract it from the reading on the scale to find the actual weight of the potatoes.