A 5kg crate falls from height of 2 m into an industrial spring scale. When the crate comes to rest the compression of the spring is 25 cm what is the spring constant?
loss of gravitational potential energy
= m g * change in height
= 5 * 9.81 *(2 + .25)
= 110 Joules
that is now stored in the spring (1/2)kx^2
so
(1/2) k (.25)^2 = 110
k = 3532 N/m
To find the spring constant, we can use Hooke's law:
F = k * x
Where:
F = force applied on the spring
k = spring constant
x = displacement (compression) of the spring
In this case, the force applied on the spring is the weight of the crate, given by:
F = m * g
Where:
m = mass of the crate (5 kg)
g = acceleration due to gravity (9.8 m/s^2)
Let's calculate F:
F = 5 kg * 9.8 m/s^2
F = 49 N
Now, we can calculate the spring constant using Hooke's law:
k = F / x
However, we need to convert the compression (25 cm) into meters.
Since 1 meter = 100 cm, the displacement (x) in meters is:
x = 25 cm / 100
x = 0.25 m
Now, we can calculate the spring constant:
k = 49 N / 0.25 m
k ≈ 196 N/m
Therefore, the spring constant is approximately 196 N/m.
To find the spring constant, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
First, let's convert the height of compression from centimeters to meters. 25 cm is equal to 0.25 m.
The force exerted by the crate is equal to its weight, which can be calculated using the formula: force = mass * gravity.
The mass of the crate is given as 5 kg, and the acceleration due to gravity is approximately 9.8 m/s².
So, the force exerted by the crate is: force = 5 kg * 9.8 m/s² = 49 N.
Now, we can calculate the spring constant using Hooke's Law.
Hooke's Law states that the force exerted by a spring is equal to the spring constant multiplied by the displacement of the spring from its equilibrium position.
In this case, the displacement of the spring is the compression of 0.25 m, and the force exerted by the crate is 49 N.
Therefore, we have: 49 N = spring constant * 0.25 m.
To find the spring constant, we can rearrange the equation as follows:
spring constant = 49 N / 0.25 m = 196 N/m.
So, the spring constant is 196 N/m.