You apply a force of 20 Nto a compressed spring that has a k= 150m
a) calculate the amount of compression
B) calculate the mass attached to the spring when moving with max speed 6m/s
For first part i got F= -- kx
x = F/ k
20/150= 0.133m
k= 150m
well, units messed up
F = - k x
20 N = -k * x
20 Newtons = -150 Newtons/ meter * x
x = -(20/150) meters
= - 0.133 meters
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one way for part B
max Kinetic energy = max potential energy
(1/2) m v^2 = (1/2) k Xmax^2
m v^2 = 150 * (-0.133)^2 = 2.65
m * 36 = 2.65
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To answer your questions, we need to first understand Hooke's Law, which states that the force applied to a spring is directly proportional to the amount the spring is stretched or compressed. The equation representing Hooke's Law is F = -kx, where F is the force applied, k is the spring constant, and x is the amount of compression or stretch.
a) To calculate the amount of compression (or stretch), we need to rearrange Hooke's Law equation to solve for x:
F = -kx
x = -F/k
Given:
Force applied (F) = 20 N
Spring constant (k) = 150 N/m
Plugging these values into the equation:
x = -F/k
x = -(20 N)/(150 N/m)
x ≈ -0.1333 m (rounded to 4 decimal places)
Therefore, the amount of compression is approximately 0.1333 meters.
b) To calculate the mass attached to the spring when moving with maximum speed, we need to use the equation for the maximum potential energy stored in a spring, which is given by the formula:
PE_max = (1/2)kx^2
Since potential energy is related to the mass and velocity, we can relate the maximum potential energy stored in the spring to the maximum kinetic energy of the mass. The equation for kinetic energy is given by:
KE_max = (1/2)mv^2
By equating the two equations, we can find the mass.
Using the same values for spring constant (k) and compression (x) from part a, and given maximum speed (v) = 6 m/s:
KE_max = PE_max
(1/2)mv^2 = (1/2)kx^2
Rearranging the equation and solving for mass (m):
m = kx^2 / v^2
m = (150 N/m)(-0.1333 m)^2 / (6 m/s)^2
m ≈ 0.0742 kg (rounded to 4 decimal places)
Therefore, the mass attached to the spring when moving with a maximum speed of 6 m/s is approximately 0.0742 kilograms.