A load of 66 N attached to a spring hanging
vertically stretches the spring 8.3 cm. The
spring is now placed horizontally on a table and stretched 11 cm.
What force is required to stretch it by this amount?
Answer in units of N.
k = 66N/8.3cm = 7.95 N/cm.
F = 11cm * 7.95N/cm =
To find the force required to stretch the spring by a certain amount, we can use Hooke's Law, which states that the force required to stretch or compress a spring is proportional to the displacement.
Hooke's Law can be written as:
F = k * x
where F is the force, k is the spring constant, and x is the displacement.
Given:
Force (F1) = 66 N
Displacement (x1) = 8.3 cm = 0.083 m
Displacement (x2) = 11 cm = 0.11 m
To find the force required to stretch the spring by x2, we need to determine the spring constant (k) first.
Using the given data, we can rearrange Hooke's Law equation to solve for the spring constant:
k = F1 / x1
Substituting the values:
k = 66 N / 0.083 m = 795.18 N/m (rounded to two decimal places)
Now, we can use the spring constant (k) to find the force required to stretch the spring by x2 using Hooke's Law equation:
F2 = k * x2
Substituting the values:
F2 = 795.18 N/m * 0.11 m
Calculating the result:
F2 = 87.47 N (rounded to two decimal places)
Therefore, the force required to stretch the spring by 11 cm is approximately 87.47 N.
To find the force required to stretch the spring by 11 cm, 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.
Hooke's Law can be expressed as:
F = -k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement of the spring.
Given that a load of 66 N stretches the spring by 8.3 cm vertically, we can calculate the spring constant (k) using the equation:
k = F / x
Plugging in the values, we get:
k = 66 N / 8.3 cm
To convert centimeters to meters, divide by 100:
k = 66 N / (8.3 cm / 100 cm/m)
Simplifying the units:
k = 66 N / 0.083 m
k = 800 N/m
Now that we have the spring constant, we can find the force required to stretch the spring by 11 cm. Plugging the values back into Hooke's Law, we have:
F = -k * x
F = -800 N/m * 0.11 m
Calculating the result:
F = -88 N
Since the force is always positive in this context, the magnitude of the force required to stretch the spring by 11 cm is 88 N.