1. A force of 720 N stretches a certain spring a distance of 15 cm. What is its force constant? If a 60-kg mass is hang on it, how far will it stretch?
k = 720N/15cm = 48N/cm
F = m*g = 60kg * 9.8N/kg = 588 N.
d = 588N/48N * 1cm = 12.25 cm.
To find the force constant (k) of the spring, we can use Hooke's Law equation:
F = k * Δx
where:
F = force applied on the spring
k = force constant
Δx = change in length of the spring
Given that a force of 720 N stretches the spring by a distance of 15 cm, we can substitute the values into the equation:
720 N = k * 15 cm
First, let's convert the distance to meters:
15 cm = 0.15 m
Now, we can rearrange the equation to solve for k:
k = 720 N / 0.15 m
k = 4800 N/m
Therefore, the force constant of the spring is 4800 N/m.
Now, to find how far the spring will stretch when a 60-kg mass is hung on it, we need to calculate the force exerted by the mass.
The force (F) exerted by the mass can be calculated using the equation:
F = m * g
where:
m = mass (60 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the values, we have:
F = 60 kg * 9.8 m/s^2
F = 588 N
Now, we can use Hooke's Law equation again to calculate the stretching distance (Δx) of the spring:
F = k * Δx
Rearranging the equation to solve for Δx:
Δx = F / k
Substituting the values:
Δx = 588 N / 4800 N/m
Δx = 0.1225 m
Therefore, the spring will stretch approximately 0.1225 meters (or 12.25 cm) when a 60-kg mass is hung on it.
To find the force constant of a spring, we can use Hooke's law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's law can be expressed using the formula: F = k * x
Where:
F is the force applied on the spring
k is the force constant (also known as spring constant)
x is the displacement or stretch in the spring
Using the given values:
F = 720 N
x = 15 cm = 0.15 m
We can rearrange the formula to solve for k:
k = F / x
Plugging in the values, we have:
k = 720 N / 0.15 m
k ≈ 4,800 N/m
The force constant (k) of the spring is approximately 4,800 N/m.
Now, to find out how far the spring will stretch when a 60-kg mass is hung on it, we can use Hooke's law once again.
The weight of the 60-kg mass can be calculated using the formula: weight = mass * acceleration due to gravity
Where:
mass = 60 kg
acceleration due to gravity = 9.8 m/s² (approximate value)
weight = 60 kg * 9.8 m/s²
weight ≈ 588 N
Since weight is a downward force and the spring stretches in the opposite direction, we need to consider the negative sign.
F = -588 N
k = 4,800 N/m
Using the Hooke's law formula again:
F = k * x
Rearranging the formula to solve for x:
x = F / k
Plugging in the values, we have:
x = -588 N / 4,800 N/m
x ≈ -0.1225 m
The spring will stretch by approximately -0.1225 m (or 12.25 cm) when a 60-kg mass is hung on it. The negative sign indicates the opposite direction of the force.