A large fish hangs from a spring balance supported from the 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?
Under what circumstances will the balance read 34.0 N? (what acceleration)
What will the balance read if the elevator cable breaks?
I will be happy to review your thinking or work on this.
If only I did know what to do...
Force= mass(totalacceleration)
= mass(acceleration upward + g)
Well, let's see if I can help you out with a little humor!
First things first, let's address the true weight of the fish. With an upward acceleration of 2.65 m/s^2, it seems the fish might be feeling a bit tingly. To calculate the true weight, we need to take into account both the upward acceleration and the force of gravity.
So, using the equation: Force = mass * acceleration, we can plug in the given values. The force we're interested in is 70.0 N, and the acceleration is the sum of 2.65 m/s^2 (upward acceleration) and the force of gravity (g).
Now, the tricky part is that pesky force of gravity. It tends to pull things down, you know? But we can approximate it using the value of 9.8 m/s^2 on Earth.
So, we have the equation: 70.0 N = mass * (2.65 m/s^2 + 9.8 m/s^2).
Solving for mass, we find: mass = 70.0 N / (2.65 m/s^2 + 9.8 m/s^2).
And that's how you calculate the true weight of the fish, my friend!
Now, as for the circumstances under which the balance reads 34.0 N, we need to find the corresponding acceleration. Let's call it "a". We'll use the same formula: Force = mass * acceleration.
Plugging in the values we have: 34.0 N = mass * (a + 9.8 m/s^2).
Solving for "a", we find: a = (34.0 N / mass) - 9.8 m/s^2.
There you have it! That's the acceleration you need to achieve in order for the balance to read 34.0 N.
Now, if the elevator cable breaks, I'm afraid things might get a little fishy! Without the support of the cable, the fish will experience a free-fall, and the balance will read 0 N. So, if you were planning on weighing the fish at that moment, I wouldn't recommend it. Just let that fish have its moment of weightlessness!
I hope that brings a smile to your face, even if I didn't have any fish jokes to offer. Keep on calculating and have a great day!
To find the true weight of the fish, we need to first consider the forces acting on it. We know that the force acting on the fish is equal to its mass multiplied by the acceleration of the elevator and the force due to gravity.
Let's denote the mass of the fish as m. The force due to gravity, which is the true weight of the fish, can be calculated using the formula:
Force gravity = mass x acceleration due to gravity
Since the fish is hanging from the spring balance and experiencing an upward acceleration, the net force acting on it is:
Net force = force gravity - force due to acceleration
We know that the net force acting on the fish is equal to the reading on the spring balance, 70.0 N:
Net force = 70.0 N
Given that the upward acceleration of the elevator is 2.65 m/s^2, we can substitute the values into the equation:
70.0 N = m x (2.65 m/s^2 + 9.8 m/s^2)
Let's simplify:
70.0 N = m x 12.45 m/s^2
To find the true weight of the fish, we need to solve for the mass. Dividing both sides of the equation by 12.45 m/s^2 gives:
m = 70.0 N / 12.45 m/s^2
m ≈ 5.62 kg
Now that we have the mass of the fish, we can calculate its true weight using the formula:
Force gravity = mass x acceleration due to gravity
Force gravity = 5.62 kg x 9.8 m/s^2
Force gravity ≈ 55.076 N
Therefore, the true weight of the fish is approximately 55.076 N.
To find the circumstances under which the balance reads 34.0 N, we can use the same formula and rearrange it to solve for the acceleration:
force due to acceleration = force gravity - reading on the balance
Substituting the values:
force due to acceleration = 55.076 N - 34.0 N
force due to acceleration = 21.076 N
Therefore, the acceleration needed for the balance to read 34.0 N is approximately 21.076 N.
If the elevator cable breaks, the elevator will be in freefall, and the acceleration will be equal to the acceleration due to gravity, which is approximately 9.8 m/s^2. In this case, the balance would read 0 N, as there would be no force acting on the fish vertically.
To find the true weight of the fish in the first situation, where the balance reads 70.0 N, we need to determine the mass of the fish and then use the equation F = mg, where F is the force (weight), m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
1. Determine the mass of the fish:
Using the equation F = ma, we can rearrange it to find mass:
mass = F / a
mass = 70.0 N / 2.65 m/s^2
mass ≈ 26.42 kg
2. Calculate the true weight of the fish:
Weight = mass × g
Weight = 26.42 kg × 9.8 m/s^2
Weight ≈ 258.8 N
Therefore, the true weight of the fish is approximately 258.8 N.
To find the circumstances under which the balance reads 34.0 N, we need to find the acceleration of the elevator.
1. Determine the mass of the fish (same as before):
mass = 26.42 kg
2. Calculate the acceleration:
Using the equation F = ma, where F is the force (reading on the balance), m is the mass, and a is the acceleration:
34.0 N = 26.42 kg × a
a ≈ 1.29 m/s^2
Therefore, in order for the balance to read 34.0 N, the elevator must have an upward acceleration of approximately 1.29 m/s^2.
If the elevator cable breaks, the elevator will experience free fall (i.e., acceleration due to gravity). In this case, the balance will read zero because there is no upward force acting on the fish.
So, if the elevator cable breaks, the balance will read zero N.