A fisherman who lives in a high rise apartment building in Toronto, weighs a fish on a spring scale and records a 11.2 N reading. He reweighs the fish while he is in his elevator and records a reading of 13.1 N. What is the acceleration of the elevator at that moment?
weight = 11.2 N = mg
=> m=11.2/9.8 = 1.143 kg
new weight = 13.1 = m(g+a)
a=13.1/1.143-9.8=1.661 m/s²
To determine the acceleration of the elevator, we first need to calculate the net force acting on the fish in both situations.
1. Outside the elevator:
The fisherman records a reading of 11.2 N on the spring scale. This reading corresponds to the weight of the fish, which is the force due to gravity acting on the fish.
So, the net force acting on the fish is 11.2 N.
2. Inside the elevator:
The fisherman records a reading of 13.1 N on the spring scale. Again, this reading corresponds to the weight of the fish.
Since the elevator is moving, there is an additional upward force acting on the fish. This additional force is equal to the product of the mass of the fish and the acceleration of the elevator.
Let's assume the mass of the fish is m kg, and the acceleration of the elevator is a m/s².
The net force acting on the fish inside the elevator is the sum of the weight of the fish and the additional upward force:
13.1 N = Weight + m * a
Since the weight of the fish is the same in both situations (11.2 N), we can rewrite the equation as:
11.2 N + m * a = 13.1 N
Now we can solve this equation to find the acceleration of the elevator (a):
m * a = 13.1 N - 11.2 N
m * a = 1.9 N
Dividing both sides of the equation by m, the mass of the fish, we get:
a = 1.9 N / m
Therefore, the acceleration of the elevator at that moment is 1.9 N/m, where m is the mass of the fish.
To find the acceleration of the elevator, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the fish is our object and the net force acting on it is the difference between the two readings on the spring scale. Let's call the mass of the fish "m" and the acceleration of the elevator "a".
According to Newton's second law:
Net force = mass * acceleration
The net force acting on the fish:
Net force = 13.1 N - 11.2 N
= 1.9 N
Now, we can rewrite Newton's second law equation:
1.9 N = m * a
To solve for "a", we need to know the mass of the fish. If we have that information, we can substitute it into the equation and solve for the acceleration.