Answer:
1.11 meters
Step-by-step explanation:
As the spring is compressed, elastic potential energy is built up in the spring. The total elastic potential energy can be found using the following formula
Ep = 1/2 x k x s²
where k = 31 N/m (spring constant)
s = 0.15 m (compression)
Ep = 3.4875 J
When the block of mass is released, the elastic potential energy (Ep) is converted to kinetic energy (Ek). From this we can find the initial velocity of the mass of block after release
Ek = 1/2 x m x u²
where Ek = Ep = 3.4875J
m = 0.08 kg (mass of block)
u = unknown (initial velocity)
u = 2.9526 m/s
Now that we know the initial velocity we need to find the deceleration of the mass of block due to friction. We will first find the force of friction from the following formula
F = ∪ x m x g
where F = unknown (frictional force)
∪ = 0.4 (coefficient of friction)
m = 0.08 kg (mass of block)
g = 9.81 m/s² (acceleration due to gravity)
F = 0.31392 N
From this force we calculate the deceleration based on the following formula
F = m x a
where F = 0.31392 (frictional force)
m = 0.08 kg (mass of block)
a = unknown (acceleration)
a = -3.924 m/s² -
*the negative sign is due to this value being deceleration
Now to find the total distance traveled we use the equation for motion
v² = u² + 2as
where v = 0 (final velocity)
u = 2.9526 m/s (initial velocity
a = -3.924 m/s² (deceleration due to friction)
s = unknown (distance traveled)
s = 1.11 meters