An object with mass m is placed against the free end of the...

An object with mass (m) is placed against the free end of the spring. From equilibrium length, which is a distance of 1.25 from the edge of the tabletop and eventually lands a distance (d) from the table top. If d = 1.60 meters, h = 1.0 meters, m = 100 g, k = 75 N/m, and x = 0.15 m, calculate the coefficient of kinetic friction for the interaction between the block and the table.

Transcript

00:01 In this question we've been told that an object is placed against one end of a compressed spring, then the spring is released and the object fall from the edge of the tabletop and travel the distance.

00:12 So we need to find out the coefficient of kinetic friction for the interaction between the block and the table.

00:17 So during when the object traveled through this distance, it encounters friction from the table.

00:25 So we need to calculate the coefficient of kinetic friction.

00:27 So in this question, we are going to use the law.

00:30 Conservation of energy.

00:32 So initially when the spring is compressed it's going to have elastic potential energy.

00:40 So when the spring is released it will gain a velocity and just when it reaches the edge of the tabletop it's going to have a velocity.

00:51 So kinetic energy, the elastic potential energy will be converted into kinetic energy of the object and some of the work done will be so on this surface there will be friction so some of this energy elastic potential energy will be lost due to friction so work done against frictional forces so this is the equation for conservation of energy so the formula for elastic potential energy is half kx square we know the spring constant k and x the compression of the spring we kinetic energy formula is half mv square in this case we know the mass but we do not we do not know the velocity we do not know the velocity just before it falls down then work done against friction the fictional forces into the distance d we know the fictional force and d so first of all we need to calculate the velocity of the block just before it falls from the edge so now when the object fall from the edge it's going to have a projectile motion so we know the distance covered so we need to find out the initial horizontal velocity we can find out this velocity using formula s equals to vt so velocity is going to be equal to this is for the horizontal velocity so we are going we are going to write for horizontal velocity because we know that when it is at the edge it's only going to have horizontal velocity there is not going to be a vertical velocity so for horizontal we can do the formula s equals to v t we need to find out the velocity so which is going to be s over t we know the distance the horizontal distance covered which is 1 .6 meters but we need to find out the time taken for the object to fall to the ground so we're going to use vertical velocity for this so for vertical velocity we need to find out the time so we are going to use the formula s equals to u t plus half 80 square so in this case we know that the initial vertical velocity is zero so this is going to be zero the distance the vertical distance covered is actually the height of the table which is 1 meter which is going to be equal to half the acceleration which will act on the object will be gravitational acceleration so 9 .8 into t square so t is going to be equal to 2 divided by 9 .8 and there's going to be a square root so the time is going to be 0 .452 seconds.

04:19 So this is the time taken for the object to fall down...

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