A light spring of constant k = 170 N/m rests vertically on the bottom of a large beaker of water. A 5.70 kg block of wood (density = 650 kg/m3) is connected to the spring and the mass-spring system is allowed to come to static equilibrium. What is the elongation, ÄL, of the spring?
im using the equation of the spring constant... F=kx F being B-weight. and i keep coming up with the wrong answer. please help me!!!
volume of wood = (5.7/650) m^3
difference in density = 1000-650 = 350 kg/m^3
net force up = 350 (5.7/650)(9.81) = 30.1 N
F = k x
30.1 = 170 x
x = 30.1/170 = .177 meter
the 1000 kg/m^3 is the density of water.
why is the difference in density 350? where does the 1000 come from?
when a 14.0 kg mass hangs from a spring that has a spring constant of 550nm the spring has a length of 82 cm. determine the length of the spring before any force is applied to it
Can someone explain this with the correct answer please.
To determine the elongation of the spring, we need to find the balance between the weight of the block and the force exerted by the spring.
First, calculate the weight of the block of wood using the formula:
Weight = mass * gravitational acceleration
Weight = (density * volume) * gravitational acceleration
Given:
Density = 650 kg/m^3
Mass = 5.70 kg
Gravitational acceleration = 9.8 m/s^2
Volume = mass / density
Volume = 5.70 kg / 650 kg/m^3
Now we can calculate the weight:
Weight = (5.70 kg / 650 kg/m^3) * 9.8 m/s^2
Next, we can determine the force exerted by the spring using Hooke's law:
F = k * x
Where:
F is the force applied by the spring (equal to the weight of the block),
k is the spring constant (given as 170 N/m),
x is the elongation of the spring.
Equating the weight of the block and the force exerted by the spring:
Weight = F
Substituting the values:
(5.70 kg / 650 kg/m^3) * 9.8 m/s^2 = 170 N/m * x
Now we can solve for x, the elongation of the spring:
x = ((5.70 kg / 650 kg/m^3) * 9.8 m/s^2) / 170 N/m
Evaluating this expression will give you the elongation of the spring, which is the answer to your question.
water density = 1,000 kg/m^3
close enough :)