A 0.50 kg mass is attached to a spring with spring constant k=43.8 N/m as shown. 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. Include a free-body diagram.
mg + k x
0.50 * 9.81 + 43.8 * 0.037
The answer---------> 6.5256<---------The answer
Is it accelerating ?
If not someone is pushing upward with that same force magnitude and the net force is zero.
To calculate the net force on the mass when the spring is compressed 3.7 cm, we first need to determine the displacement of the spring from its unstretched position.
Given:
Mass of the object (m) = 0.50 kg
Spring constant (k) = 43.8 N/m
Compression distance of the spring (x) = 3.7 cm = 0.037 m
Now, let's analyze the free-body diagram:
1. Gravitational force (mg):
The weight of the mass acts downward and can be represented by the formula: Fg = mg.
Fg = (0.50 kg) * (9.8 m/s²) = 4.9 N
2. Spring force (Fs):
When the spring is compressed, it exerts a force in the opposite direction to the displacement.
According to Hooke's law, the force exerted by a spring is given by: Fs = -kx,
where k is the spring constant and x is the displacement from the equilibrium position.
In this case, x = -0.037 m (negative because it is compressed).
Fs = -(43.8 N/m) * (-0.037 m) = 1.6226 N
3. Net force (Fnet):
The net force is the vector sum of all the forces acting on the object.
Fnet = Fg + Fs = 4.9 N + 1.6226 N = 6.5226 N
Therefore, the net force on the mass when the spring is compressed 3.7 cm is 6.5226 N.