A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters.
Which expression represents the spring constant? (1 kg=9.8 N)
-4k / cm
-4/19.6 N
-19.6N / 4
-4 cm/ k
F = m g = k x
2*9.8 = k * 0.04
19.6 = k * 0.04
k = 19.6 / 0.04 Newtons/meter = 19.6/4 Newtons/ centimeter
To find the spring constant, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring.
In this case, the displacement of the spring is 4 centimeters, which is equivalent to 0.04 meters (1 meter = 100 centimeters).
The weight of the cat recorded is 2 kilograms, which can be converted to Newtons using the conversion factor 1 kg = 9.8 N.
Therefore, the force exerted by the spring can be calculated as follows:
Force = weight = mass × gravitational acceleration
Force = 2 kg × 9.8 N/kg
Force = 19.6 N
Now, we can plug these values into Hooke's Law:
Force = spring constant × displacement
19.6 N = spring constant × 0.04 m
Rearranging the equation to solve for the spring constant, we have:
spring constant = 19.6 N / 0.04 m
Simplifying the expression, we get:
spring constant = 490 N/m
Therefore, none of the given options correctly represents the spring constant.
To determine 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. Mathematically, it can be written as:
F = kx
Where:
F is the force exerted by the spring
k is the spring constant
x is the displacement of the spring from its equilibrium position
In this case, the displacement of the spring is given as 4 centimeters. To find the force, we need to convert the weight of the cat from kilograms to newtons.
Given that 1 kg = 9.8 N, the weight of the cat is:
Weight = 2 kg * 9.8 N/kg = 19.6 N
Now, we have the force (F = 19.6 N) and the displacement (x = 4 cm). By rearranging Hooke's Law, we can solve for the spring constant (k):
k = F / x
k = 19.6 N / 4 cm
However, we need to convert centimeters to meters because the units of force are newtons and the units of displacement must match. There are 100 centimeters in 1 meter, so:
k = 19.6 N / (4 cm / 100 cm/m)
Simplifying the expression:
k = 19.6 N / 0.04 m
k = 490 N/m
Therefore, the correct expression for the spring constant is -19.6N / 4 (option c).