A large fish hangs from a spring balance supported from the roof of an elevator.
If the elevator has an upward acceleration of 2.85m/s^2 and the balance reads 60.0N , what is the true weight of the fish?
Under what circumstances will the balance read 39.0N ?
True Weight of fish:
F= ma + mg
Where:
F=60.0N
a=2.85 m/s^s
g=9.80 m/s^2
Plug into formula where you are solving for m:
F = ma + mg
60.0 N = (2.85)m + (9.80)m
60.0 N = (12.65)m
m= 60.0N/12.65
m= 4.74 kg => 4740 g => 46.5 N
Under what circumstances will the balance read 39.0 N?
Formula: ∑F = F(normal) + F(weight)
Where:
∑F= a(4.74kg)
F(normal)= 39.0 N
F(weight)=(-9.80m/s^2)(4.74kg)
Plug into formula:
∑F = F(normal) + F(weight)
a(4.74) = 39.0 N + (-9.80)(4.74)
a(4.74) = -7.452
a = -1.57 m/s^2
thanks
Well, let's first calculate the apparent weight of the fish in the elevator. We can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The net force acting on the fish in the elevator is equal to its true weight minus the force due to the upward acceleration of the elevator. So we have:
Net force = True weight - Force due to acceleration
Given that the force due to the acceleration is equal to the mass of the fish multiplied by the acceleration, we can write:
Net force = True weight - (mass of fish x acceleration)
Now let's substitute the values given:
60N = True weight - (mass of fish x 2.85m/s^2)
To find the true weight of the fish, we need to know its mass. However, this information is not provided in the given question, so unfortunately, we cannot determine the true weight of the fish.
As for when the balance will read 39.0N, well, that would occur when the net force acting on the fish is 39.0N. Again, we would need the mass of the fish to calculate this, which is not provided in the question. So, we don't have enough information to determine the circumstances under which the balance would read 39.0N.
I apologize for not being able to provide a more humorous answer this time. Sometimes, the laws of physics can be quite serious!
To find the true weight of the fish, we need to address two forces acting on it: the force of gravity and the force due to the elevator's acceleration.
1. Force due to gravity:
The force due to gravity is equal to the weight of the fish and is given by the equation Fg = mg, where m is the mass of the fish and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Force due to elevator's acceleration:
The force due to the elevator's acceleration is given by the equation Fe = ma, where m is the mass of the fish and a is the acceleration of the elevator.
To find the true weight of the fish, we need to subtract the force due to the elevator's acceleration from the reading on the spring balance:
True Weight = Reading on the spring balance - Force due to elevator's acceleration
1. The force due to gravity remains the same, so we can write Fg = mg.
2. Considering the upward acceleration of the elevator, we can write Fe = ma.
Given:
Upward acceleration of the elevator, a = 2.85 m/s^2
Reading on the spring balance, F = 60.0 N
From step 2, we have Fe = ma.
Plugging in the values, we have:
60.0 N = m(2.85 m/s^2)
Solving for m, we get:
m = 60.0 N / 2.85 m/s^2
m ≈ 21.05 kg
Now, we can find the true weight by substituting the values of m and g in the equation Fg = mg:
Fg = (21.05 kg)(9.8 m/s^2)
Fg ≈ 206.35 N
Therefore, the true weight of the fish is approximately 206.35 N.
To find the circumstances under which the balance will read 39.0 N, we need to set up the equation as follows:
Reading on the spring balance - Force due to elevator's acceleration = 39.0 N
Using the same approach as above, we can solve for the upward acceleration of the elevator:
39.0 N = m(a + g)
Substituting the known values:
39.0 N = (21.05 kg)(a + 9.8 m/s^2)
Solving for a, we find:
a + 9.8 m/s^2 = 39.0 N / 21.05 kg
a + 9.8 m/s^2 ≈ 1.854 m/s^2
Therefore, the elevator must have an upward acceleration of approximately 1.854 m/s^2 for the balance to read 39.0 N.
To find the true weight of the fish, we first need to understand the forces acting on it.
When the elevator is at rest or moving with constant velocity, the fish experiences two forces: its weight (mg) pulling it downward and the tension in the spring balance pulling it upward.
Let's denote the mass of the fish as m. We know that the acceleration of the elevator is 2.85 m/s^2 and the spring balance reads 60.0 N. The tension in the spring balance is equal to the sum of the weight of the fish and the force due to the acceleration of the elevator.
So we have:
Tension = Weight of the fish + Force due to acceleration
Tension = 60.0 N
Force due to acceleration = m * acceleration
Now, the weight of the fish is simply the force due to gravity, which can be calculated using the formula:
Weight = mass * gravitational acceleration
To find the true weight of the fish, we can substitute the values into the equation:
60.0 N = Weight + (m * 2.85 m/s^2)
Weight = (60.0 N) - (m * 2.85 m/s^2)
Weight = 60.0 N - 2.85 m/s^2 * m
So, the true weight of the fish can be calculated by subtracting the force due to acceleration from the tension measured by the spring balance.
To find when the balance will read 39.0 N, we can use a similar approach. We substitute 39.0 N for the tension in the equation and solve for the weight of the fish:
39.0 N = Weight + (m * 2.85 m/s^2)
Weight = 39.0 N - 2.85 m/s^2 * m
Now, we can use this equation to find the weight of the fish when the balance reads 39.0 N.
Note that the true weight of the fish is the force due to gravity, so if the elevator is not accelerating and the balance reads 39.0 N, then the weight of the fish is simply 39.0 N.
I hope this helps! Let me know if you have any further questions.