A fish hangs from a spring scale supported from the roof of an elevator. a) if the elevator has an upward acceleration of 1.2 m/s^2 and the scale reads 200 N, what is the true force of gravity on the fish? b) under what circumstances will the scale read 150 N? c) what will the scale read if the elevator cable breaks?
solve for mg:
200=mg(9.8+1.2)
b. 250=mg(9.8-a) solve for a using mg from a).
c. cable breaks, it is in free fall, scale=0
a) Well, it seems like this fish has caught quite the ride! To find the true force of gravity on the fish, we need to take into account the upward acceleration of the elevator. Since the scale reads 200 N, we need to subtract the force due to the acceleration to find the force of gravity on the fish. So, using a bit of Newtonian math, we have:
True force of gravity = Scale reading - Force due to acceleration
True force of gravity = 200 N - (mass of the fish * acceleration due to gravity)
b) Ah, the scale seems to be feeling a little lighter, doesn't it? If the scale reads 150 N, then we need to consider the force due to the acceleration of the elevator. This time, we need to add the force due to the acceleration to the force of gravity on the fish. Thus, we have:
Scale reading = True force of gravity + Force due to acceleration
150 N = True force of gravity + (mass of the fish * acceleration due to gravity)
c) Uh-oh, it looks like things are about to go fishy! If the elevator cable breaks, well, I hate to break it to you, but the scale won't exactly be able to help us out. Without the support of the elevator, the scale won't be able to measure the force acting on the fish. In simpler terms, the scale reading will be zilch, zero, nada! Just like the cable, it's a total breakdown!
Keep swimming with those physics questions!
a) To find the true force of gravity on the fish, you need to consider the acceleration of the elevator and the reading on the scale.
Using Newton's second law (F = m * a), we can calculate the mass of the fish:
F = m * a
200 N = m * 1.2 m/s^2
Rearranging the equation:
m = 200 N / 1.2 m/s^2
m ≈ 166.67 kg
The mass of the fish is approximately 166.67 kg.
Now, to find the true force of gravity, we can use the equation F = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2):
F = m * g
F = 166.67 kg * 9.8 m/s^2
F ≈ 1633 N
Therefore, the true force of gravity on the fish is approximately 1633 N.
b) The scale will read 150 N when the force of gravity on the fish is balanced by a combination of the upward force due to the elevator's acceleration and the force of gravity. In other words, the net force acting on the fish is zero.
So, the equation becomes:
Fnet = m * a - Fg = 0,
where Fnet is net force, m is the mass of the fish, a is the acceleration of the elevator, and Fg is the force of gravity.
Solving for Fg:
Fg = m * a
Fg = 166.67 kg * 1.2 m/s^2
Fg ≈ 200 N
Therefore, when the scale reads 150 N, the force of gravity on the fish is approximately 200 N.
c) If the elevator cable breaks, the fish and the scale will experience free fall, causing the acceleration to be equal to the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the scale will read zero, as there is no force exerted on the fish by the scale.
So, if the elevator cable breaks, the scale will read zero.
To answer these questions, we need to consider the forces acting on the fish in different scenarios and apply Newton's second law of motion. Here's how we go about solving each part:
a) If the elevator has an upward acceleration of 1.2 m/s^2 and the scale reads 200 N, we first need to determine the net force acting on the fish. The net force is the difference between the force exerted by the spring scale and the force of gravity.
To calculate the force of gravity on the fish, we can use the equation:
force of gravity = mass * acceleration due to gravity
Assuming the acceleration due to gravity is approximately 9.8 m/s^2, the force of gravity can be determined by:
force of gravity = mass * 9.8
Now, since the fish is in an elevator with an upward acceleration, we need to account for this upward force. The net force acting on the fish can be calculated by:
net force = force of gravity - upward force
Given that the scale reads 200 N, we know that the net force is 200 N. Therefore, we can write:
200 N = force of gravity - upward force
Since the elevator acceleration is upward, the upward force can be calculated by:
upward force = mass * acceleration
Now we have two equations:
force of gravity = mass * 9.8
200 = force of gravity - mass * acceleration
We can solve these equations simultaneously to find the true force of gravity on the fish.
b) To determine under what circumstances the scale reads 150 N, we need to consider the forces acting on the fish in a scenario where the scale reads 150 N.
Similar to part a, we need to determine the net force acting on the fish. Since the scale reading is now 150 N, the net force becomes 150 N. Using the same equation as before:
net force = force of gravity - upward force
We need to solve this equation to find the conditions under which the scale reads 150 N.
c) If the elevator cable breaks, the elevator will be in free fall. This means that the acceleration acting on the fish will be equal to the acceleration due to gravity (9.8 m/s^2) and directed downward. Under free fall, the scale will register the force of gravity acting on the fish, which can be determined using the equation:
force of gravity = mass * 9.8
Thus, the scale reading when the elevator cable breaks will be the force of gravity on the fish.
By following these steps and solving the appropriate equations, you can find the answers to each of the given questions.