A mass m = 16 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 16 kg is pulled along a horizontal floor with NO friction for a distance d =8.2 m. Then the mass is pulled up an incline that makes an angle = 38° with the horizontal and has a coefficient of kinetic friction k = 0.47. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 38° (thus on the incline it is parallel to the surface) and has a tension T =90 N.

1) What is the work done by tension before the block goes up the incline? (On the horizontal surface.)

2) What is the speed of the block right before it begins to travel up the incline?

3) What is the work done by friction after the block has traveled a distance x = 5.3 m up the incline? (Where x is measured along the incline.)

4) What is the work done by gravity after the block has traveled a distance x = 5.3 m up the incline? (Where x is measured along the incline.)

5) How far up the incline does the block travel before coming to rest? (Measured along the incline.)

PLEASE SHOW STEPS

Explanation / Answer

mass m = 16 kg

pulled along a horizontal floor with NO friction for a distance d =8.2 m.

1) The work done by tension before the block goes up the incline is

Work Done = Force * displacement = 90 N * 8.2 m = 738 joule.

2) The speed of the block right before it begins to travel up the incline is

From work energy theorem

Kinetic Energy of tha mass at this instant = Work done by tension till then = 738 joule

or 1/2 MV2 = 738

or V2 = 738*2 / 16 = 369/4 = 92.25

or V = 9.6 m/s .

3) The work done by friction after the block has traveled a distance x = 5.3 m up the incline will be

Work Done = Force * Displacement = - kMg Cos(38) * 5.3 = -0.47 * 16 *9.8*(4/5)*5.3 where g= acceleraion due to gravity=9.8m/s2

= - 312.47 joule

Work done by friction is negative because displacement is in opposite direction of friction force.

4) The work done by gravity after the block has traveled a distance x = 5.3 m up the incline will be

Work done by gravity = Force * displacement = -Mg*(5.3Sin(38)) Since gravitational forcre is vertical so vertical displacement i.e. 5.3 Sin(38) will be taken as displacement for this

= - 16* 9.8*5.3*(3/5)

= 498.62 joule

Here also work done by gravity is negative because force and displacement are in opposite direction.

5) The block travel before coming to rest on incline until its velocity becomes zero on inclined plane .

Let X meter be the distance nefore coming to rest

Again work energy theorem

Initial kinetic Energy + work done by rope on incline +work done by friction + work done by gravity= 0

738 + 90*X - 73.69*X - 94.08X =0

or X = 738/ (77.77) = 9.49 m.

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