# Physics spring balance problem?

A large fish hangs from a spring balance supported from the roof of an elevator (strange, I know).

a) If the elevator has an upward acceleration of 2.90 m/s^2 and the balance reads 50.0 N, what is the true weight of the fish?

b) Under what circumstances will the balance read 34.0 N?

acceleration of the elevator = ____________ m/s^2

Homework problem that is literally killing me hour by hour.

Relevance

Force = weight + mass x acceleration

Force = mass x g + mass x acceleration

F = m(g + a)

50.0 = m(9.81 + 2.90)

m = 50.0/(12.71) = 3.93... kg

weight = mass x g = 3.93... x 9.81 = 38.6 N

(b)

34.0 = 3.93...(9.81 + a)

a = 34.0/3.93... - 9.81 = -1.1672 m/s^2

The elevator would be accelerating downwards at 1.1672 m/s^2.

There are two ways in which a NORMAL elevator could accelerate downward. (Of course an elevator with a large fish hanging from the ceiling is not normal.)

1) The elevator could go from being stopped to starting to go down. This is an acceleration downwards.

2) The elevator could be going up and come to a stop. This is also negative acceleration. Its speed up is decreasing.

• Spring Balance Physics

• Ya, strange indeed. Tell him to use a weighing machine instead :P

ok, so here's the solution....

a) Use the 2nd law of motion and write down the forces acting on that fish. Since the acceleration is upwards thus there's a net force that acts upwards. So if you draw a free body diagram of the fish then forces acting on it are would be.

1)Force due to spring balance upwards F

2) Its weight W downwards. then

F-W= M a ( where M is mass of fish and a is acceleration i.e 2.9m/s^2)

Since M= W/g hence

F= W( a/g+1)

=>W= F*g/(a+g)

you know that spring balance reads 50N i.e F=50N

g= is acceleration due to gravity

and a is already known to u so u can calculate W.

b)

Use the above equation again i.e F-W= W*a/g ( I wrote M= W/g directly)

As you know the true weight W from part a and F is given 34.N you can calculate a.

1 thing must be clear though ,

The above equation was written assuming that the elevator moves up, however in case acceleration comes out to be negative using above equation that means our assumption was incorrect and this condition would occur when elevator would be coming down. So you need to write the direction also where the elevator is moving.

Hope that helps :)

• The spring constant is given as 25 N/m The rock causes the spring to extend 0.072 m. You goal is to get an answer in Newtons (N), so N= N/m * m = N = 25 N/m * 0.072m = 1.8 Newtons of force By the way Newtons = mass * gravity, so the mass of the stone is about 183 grams. Assuming 9.8 m / s^2 for gravity. Where I am in Tucson, it is more like 9.797 m / s^2.

• elevator = instantaneous acceleratoin

obj on scale = uniform motion

w = a * m

m=w/a

50/2.90 = 17.2413793kg (rounded = 17.24kg)

elevator on way down g-a due to motion of scales

(not needed, but good to know)

AND

elevator on way up g+a

9.8+2.9 = 6.9

scale reading = 6.9*17.24 = 118.95600N (rounded 118.96N)

34/9.8 = 3.46938776kg (rounded 3.47kg)

34N = Fg*3.47kg

34/3.47 = Fg

Fg = 9.79827089

g= 9.81

9.81 - 9.79827089 = 0.01172911

acceleration = .012 m/s^2

? that was my attempt :)

• Gravity is accelerating your fish down at 32ft/s/s.

The elevator is adding 9.5144 ft/s/s or 0.2973G to the reading of 11.25 lb

so the fish weighs 11.25/1.2973 = 8.672 lb or 38.542 N

To appear to weigh 7.65 lb, the elevator needs to accelerate at 0.882G or -4.0612 ft/s/s (down) or -1.2378 m/s/s