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?
F=ma
13.1-11.2=11.2/g * a solve for a
To determine the acceleration of the elevator, we can use 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).
In this scenario, the fisherman weighing the fish is experiencing two forces: the force due to gravity (weight of the fish) and the force due to the elevator's acceleration.
Let's break down the problem step by step:
Step 1: Calculate the mass of the fish.
Since the force of gravity is measured in newtons and weight is simply the force of gravity acting on an object, we can use the equation W = m*g, where W represents weight, m represents mass, and g represents the acceleration due to gravity (approximately 9.8 m/s^2). Rearranging the equation, we have m = W/g.
m = 11.2 N / 9.8 m/s^2
m = 1.14 kg
Step 2: Calculate the net force acting on the fish while inside the elevator.
The net force acting on the fish is the difference between the weight of the fish and the force exerted by the elevator. The reading on the scale inside the elevator is 13.1 N, which represents the net force.
net force = 13.1 N - weight of the fish
net force = 13.1 N - (1.14 kg * 9.8 m/s^2)
net force = 13.1 N - 11.19 N
net force = 1.91 N
Step 3: Calculate the acceleration of the elevator.
Using Newton's second law of motion, we can rearrange the formula to calculate acceleration: a = F/m, where F is the net force and m is the mass of the fish.
a = net force / m
a = 1.91 N / 1.14 kg
a ≈ 1.67 m/s^2
Therefore, the acceleration of the elevator at that moment is approximately 1.67 m/s^2.