an object of mass m is being weighed in an elevator that is moving upward with an acceleration a. What is the eesult if the weighing is done using a spring balance and a pan balance?
With a spring balance, there is an additional tension ma upwards, therefore
the registered weight
= mg+ma=m(g+a)
With a pan balance (one pan object, the other weights)
Both sides experience the same acceleration,
so will exert equally m(g+a) on each side.
Hence it will show true mass.
When an object of mass m is being weighed in an elevator that is moving upward with an acceleration a, the apparent weight of the object will be different than its actual weight. The measured weight will depend on whether a spring balance or a pan balance is used.
1. Spring Balance:
A spring balance measures the force exerted on it, which is proportional to the weight of the object. To find the apparent weight of the object using a spring balance, we need to consider the net force acting on the object.
The forces acting on the object in the elevator are:
- Gravitational force (mg), which is the actual weight of the object downward.
- Normal force (N) exerted by the spring balance upward.
- Inertial force (ma) due to the upward acceleration of the elevator.
Since the object is in equilibrium (not accelerating vertically), the net force in the vertical direction is zero:
N - mg - ma = 0
The apparent weight measured by the spring balance (N) can be determined by rearranging the equation as follows:
N = mg + ma
Therefore, if the weighing is done using a spring balance, the apparent weight of the object will be the sum of its actual weight (mg) and the additional weight due to the upward acceleration (ma).
2. Pan Balance:
A pan balance measures the balance between the weights on two sides. To find the apparent weight of the object using a pan balance, we need to consider the net force acting on the object and the pan balance.
The forces acting on the object in the elevator and the pan balance can be broken down into different components:
- Gravitational force (mg), which is the actual weight of the object downward.
- Normal force (N) exerted by the pan balance upward.
- Inertial force (ma) due to the upward acceleration of the elevator.
- Reaction force (R) exerted by the pan balance on the object.
Similar to the spring balance case, the object is in equilibrium (not accelerating vertically), so the net force in the vertical direction is zero:
N - mg - ma = 0
The apparent weight measured by the pan balance is given by the normal force (N). Since the equilibrium equation gives N = mg + ma, the apparent weight measured by the pan balance will also be the sum of the object's actual weight (mg) and the additional weight due to the upward acceleration (ma).
Therefore, whether the weighing is done using a spring balance or a pan balance, the apparent weight of the object will be the sum of its actual weight and the additional weight due to the upward acceleration.