A 0.50 kg mass is attached to a spring with spring constant, k= 43.8N/m. Suppose the mass is
pushed upward, so that it rises past the spring’s unstretched position, compressing the spring. Calculate the
net force on the mass when the spring is compressed 3.7 cm.
mg + k x
0.50 * 9.81 + 43.8 * 0.037
To calculate the net force on the mass when the spring is compressed, we need to use Hooke's Law.
Hooke's Law states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be written as:
F = -kx
Where:
F is the force exerted by the spring,
k is the spring constant (given as 43.8 N/m),
x is the displacement from the equilibrium position.
In this case, the spring is compressed by 3.7 cm, which is equivalent to 0.037 m. Substituting the values into the equation, we get:
F = -(43.8 N/m)(0.037 m)
= -1.6176 N
Therefore, the net force on the mass when the spring is compressed 3.7 cm is approximately -1.6176 N.
To calculate the net force on the mass when the spring is compressed, you need to use Hooke's Law.
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is:
F = -kx
Where:
F is the force exerted by the spring,
k is the spring constant (given as 43.8 N/m),
x is the displacement from the equilibrium position (given as 3.7 cm or 0.037 m).
Substituting the given values into the formula, we can calculate the net force:
F = -kx
F = -(43.8 N/m)(0.037 m)
F = -1.6206 N
The negative sign indicates that the force is in the opposite direction of the displacement (towards the equilibrium position). Therefore, the net force on the mass when the spring is compressed 3.7 cm is approximately -1.6206 N.