A block of mass m = 353 g is dragged with a string across a rough horizontal tab

Question

A block of mass m = 353 g is dragged with a string across a rough horizontal table. The string tension is T= 3.11 N, and it pulls upward at an angle of phi = 48.0 degree with the horizontal. At one particular instant the block is moving at a speed of v = 5.70 m/s. The coefficient of kinetic friction between the block and the table is mu k = 0.699. What is the power supplied to the block by the string tension? What is the power supplied by the force of friction? At this instant the block's speed is

Explanation / Answer

here,

mass of block = 356g = 0.356 Kg
speed of block = 5.70 m/s
uk = 0.699

Writing TEnsion in string in respective components.

Tx = Tcos48 = 3.11 *0.669 = 2.08 N
Ty = TSin48 = 3.11 * 0.743 = 2.311 N

as,
From newton law of motins we have
Fnet = 0

PART A:

for Force in X direction
Tx - Ff
Power Supplied = Force * Velocity
P = (Tx - Ff)*5.70
P = (2.08 - uk*(mg+Tsin48) ) * 570
P = (2.08 - 0.734) * 5.70
P = 11.77 Watt

The Power delivered by String Force will be equal to 11.77 Watt

PART B:
for Force in Y direction
Fn -mg + Tsin48 = 0

Where,
Fn is Normal Force

Fn = mg - Tsin48
Fn = (0.343 *9.8) - 2.311
Fn = 1.05 N

Therefore
Ff = uK*Fn = 0.699 * 1.050
Ff = 0.734 N
Power Delivered By Frictional Force will be :

power = Force * Velocity
P = 0.734 *5.70
P = 4.183 Watt

The power deliverd by Frictional Force will be 4.183 Watt

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