*I really don't know how to get started. I have done lots of the homework, but this one (and a couple of others) are really giving me PROBLEMS.*
A large fish hangs from a spring balance supported fromthe roof of an elevator.
If the elevator has an upward acceleration of 2.65 m/s^2 and the balance reads 70.0 N, what is the true weight of the fish?
Answer should be expressed in N.
Under what circumstances will the balance read 34.0 N?
Answer should be expressed in m/s^2.
What will the balance read if the elevator cable breaks?
Answer should be expressed in N.
To solve these problems, we need to consider the forces acting on the fish in different situations. Let's break it down step by step:
1. When the elevator is at rest:
In this case, the fish is not experiencing any acceleration, so the net force acting on it is zero. Therefore, the true weight of the fish is equal to the reading on the balance, which is 70.0 N.
2. When the elevator accelerates upward:
In this situation, we need to consider the additional force caused by the elevator's acceleration. The net force acting on the fish will be the sum of its weight and the force caused by the acceleration. We can use Newton's second law to calculate this:
Net force = ma
In this case, the mass (m) of the fish cancels out, so we have:
Net force = weight of the fish + force due to acceleration
Since the weight of the fish is equal to 70.0 N (as determined in the previous case), we can subtract it from the net force to find the force caused by the acceleration. Rearranging the formula, we have:
Force due to acceleration = Net force - weight of the fish
= 70.0 N - 70.0 N
= 0 N
This means that in the scenario where the elevator is accelerating upward with 2.65 m/s^2, the balance will read zero, indicating that the fish is in a weightless state during the acceleration.
3. When the balance reads 34.0 N:
To determine this, we need to calculate the acceleration of the elevator. Once we have the acceleration, we can use the same approach as in case 2 to find the true weight of the fish.
Using Newton's second law again:
Net force = weight of the fish + force due to acceleration
Since we know that the balance reads 34.0 N, we can substitute this as the net force into the formula. Rearranging the formula, we have:
Force due to acceleration = Net force - weight of the fish
= 34.0 N - 70.0 N
= -36.0 N
The negative sign indicates that the force due to acceleration is in the opposite direction to the weight of the fish. To find the acceleration, we can rearrange the formula:
Force due to acceleration = m * a
Where m is the mass of the fish. Rearranging the formula for acceleration, we have:
a = (Force due to acceleration) / m
= (-36.0 N) / m
This means that in order for the balance to read 34.0 N, the elevator's acceleration must be -36.0 N/m, or -36.0 m/s^2 (since force is measured in Newtons and mass is measured in kilograms).
4. When the elevator cable breaks:
In this situation, the elevator is in free fall, which means the acceleration is equal to the acceleration due to gravity (9.8 m/s^2). Therefore, the net force acting on the fish is equal to its weight:
Net force = weight of the fish
Since we established earlier that the weight of the fish is 70.0 N, the balance will read 70.0 N.