Question

A wooden block with mass 1.05 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 35.0 degrees (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 4.90m up the incline from A, the block is moving up the incline at a speed of 5.10 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is 0.55. The mass of the spring is negligible. Calculate the amount of potential energy that was initially stored in the spring.

Answer 1

Answer:

Explanation:

energy stored in spring initially

= kinetic + potential energy of block + energy dissipated by friction

= 1/2 mv² + mgh + μ mgcosθ x  d

m is mass , v is velocity at top position , h is vertical height , μ is coefficient of friction ,θ is angle of inclination of plane

= m (1/2 v² + gh + μ gcosθ x  d )

= 1.05 ( .5 x 5.1² + 9.8 x 4.9 sin35 + .55 x 9.8 cos35 x 4.9 )

= 1.05 ( 13.005 + 27.543 + 21.635)

= 65.3 J .

Answer 2

The amount of potential energy that was initially stored in the spring due to the wooden block is 65.3 joules.

What is potential energy?

Potential energy is the energy which body posses because of its position.

The potential energy of a body is given as,

$PE=mgh$

Here, (m) is the mass of the body, (g) is the gravitational force and (h) is the height of the body.

The energy stored in the spring is the sum of all the potential energy, kinetic energy and the energy dissipated due to friction. Therefore, it can be given as,

$E=mgh+\dfrac{1}{2}mv^2+\mu mgd\cos\theta$

Here, the mass of the wooden block is 1.05 kg . Angle of inclination is  35.0 degrees (point A). The distance from point B is 4.90m up the incline from A.

The speed of the block is 5.10 m/s and the coefficient of kinetic friction between the block and incline is 0.55. Therefore, put the values in the above formula as,

$E=1.05(9.81)(4.9\sin(35))+\dfrac{1}{2}(1.05)(5.1)^2+(0.55)(1.05)(9.8)(4.9)\cos(35)\\E=65.3\rm J$

Hence, the amount of potential energy that was initially stored in the spring due to the wooden block is 65.3 joules.

Learn more about the potential energy here;

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