Final answer:
The true weight of the fish in an elevator accelerating upward can be found by first calculating the mass from the apparent weight and then using gravitational force to find the actual weight. The true weight is found to be 48.0 N.
Step-by-step explanation:
The student is asking about the true weight of a fish that is being weighed in an elevator that is accelerating upwards. To find the true weight, we need to account for both the gravitational force and the additional force due to the elevator's acceleration.
The balance reading represents the apparent weight of the fish, which is a combination of its true weight and the force due to the elevator's acceleration. The formula for the apparent weight (Fapparent) when the elevator is accelerating upwards is:
Fapparent = m(g + a)
where:
- m is the mass of the fish,
- g is the acceleration due to gravity (9.8 m/s2), and
- a is the acceleration of the elevator (2.45 m/s2).
Since we are given Fapparent as 60 N, we can rearrange the equation to solve for m:
m = Fapparent / (g + a)
m = 60 N / (9.8 m/s2 + 2.45 m/s2)
m = 60 N / 12.25 m/s2
m = 4.9 kg
The true weight (Ftrue) is the gravitational force on the mass, which is:
Ftrue = m * g
Ftrue = 4.9 kg * 9.8 m/s2
Ftrue = 48.02 N
The true weight, rounded to two significant figures as the numbers provided in the question, is 48.0 N, which corresponds to option C.