- #1
kris8969
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A spring is mounted at an angle of theta = 39degrees on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 4.9 kg up the incline.
(a) If the spring constant is 580 N/m, how fast is the mass moving when leaves the spring?
m/s
[5 points] 5 attempt(s) made (maximum allowed for credit = 5)
[after that, multiply credit by 0.5 up to 10 attempts]
1.864 NO
(b) To what maximum distance from the starting point will the mass rise up the incline?
m
i have no clue what is correct because i have tried so many different ones
Step One
=======
Find the Force created by the spring
F = kx
k = 580 N/m
x = 15cm = 15*[1 m/100 cm] = 0.15 m
F = 580*0.15 = 87 N
Step Two
=======
Find the force created (in opposition) by the mass trying to slide down the incline.
The formula for the force trying to go down the incline is F = mg*sin(A)
A = 39o
m = 4.9 kg
g = 9.81 m/s^2
F-incline = 4.9*9.81 * sin(28)
F-incline = 30.25 N
Step Three
========
Find the net upward force created by the spring.
F-net = F-spring - F-incline
F-net = 87 - 30.25= 56.75
Step Four
=======
Find the acceleration.
F = m*a
56.75 = 4.9*a
11.58 m/s^2 = a
Step Four
=======
Find the final velocity of the mass as it departs from the spring.
vi = 0
a = 11.58
d = 0.15 m
vf = ??
vf^2 = vi^2 + 2*a*d
vf^2 = 0 + 2*11.58*0.15
vf^2 = 3.47
vf = 1.86 m/s
(a) If the spring constant is 580 N/m, how fast is the mass moving when leaves the spring?
m/s
[5 points] 5 attempt(s) made (maximum allowed for credit = 5)
[after that, multiply credit by 0.5 up to 10 attempts]
1.864 NO
(b) To what maximum distance from the starting point will the mass rise up the incline?
m
Homework Equations
i have no clue what is correct because i have tried so many different ones
The Attempt at a Solution
but for some reason this is not the correct answerStep One
=======
Find the Force created by the spring
F = kx
k = 580 N/m
x = 15cm = 15*[1 m/100 cm] = 0.15 m
F = 580*0.15 = 87 N
Step Two
=======
Find the force created (in opposition) by the mass trying to slide down the incline.
The formula for the force trying to go down the incline is F = mg*sin(A)
A = 39o
m = 4.9 kg
g = 9.81 m/s^2
F-incline = 4.9*9.81 * sin(28)
F-incline = 30.25 N
Step Three
========
Find the net upward force created by the spring.
F-net = F-spring - F-incline
F-net = 87 - 30.25= 56.75
Step Four
=======
Find the acceleration.
F = m*a
56.75 = 4.9*a
11.58 m/s^2 = a
Step Four
=======
Find the final velocity of the mass as it departs from the spring.
vi = 0
a = 11.58
d = 0.15 m
vf = ??
vf^2 = vi^2 + 2*a*d
vf^2 = 0 + 2*11.58*0.15
vf^2 = 3.47
vf = 1.86 m/s