A wooden block with mass 1.60 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 30.0° (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 6.55 m up the incline from A, the block is moving up the incline at a speed of 7.50 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is [tex]\mu_k[/tex] = 0.50. The mass of the spring is negligible.
Calculate the amount of potential energy that was initially stored in the spring. Take free fall acceleration to be 9.80 m/s².

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CarliReifsteck CarliReifsteck · Answer 1 · 2020-03-16T07:23:01+01:00

Answer:

The amount of potential energy that was initially stored in the spring is 88.8 J.

Explanation:

Given that,

Mass of block = 1.60 kg

Angle = 30.0°

Distance = 6.55 m

Speed = 7.50 m/s

Coefficient of kinetic friction = 0.50

We need to calculate the amount of potential energy

Using formula of conservation of energy between point A and B

[tex]U_{A}+k_{A}+w_{A}=U_{B}+k_{B}[/tex]

[tex]U_{A}+0-fd=mgy+\dfrac{1}{2}mv^2[/tex]

[tex]U_{A}=\mu mg\cos\theta\times d+mg h\sin\theta+\dfrac{1}{2}mv^2[/tex]

Put the value into the formula

[tex]U_{A}=0.50\times1.60\times9.8\cos30\times6.55+1.60\times9.8\times6.55\sin30+\dfrac{1}{2}\times1.60\times(7.50)^2[/tex]

[tex]U_{A}=88.8\ J[/tex]

Hence, The amount of potential energy that was initially stored in the spring is 88.8 J.