A mass m = 13 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =7.4 m. Then the mass is pulled up an incline that makes an angle = 32° with the horizontal and has a coefficient of kinetic friction k = 0.31. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 32° (thus on the incline it is parallel to the surface) and has a tension T =60 N. How far up the incline does the block travel before coming to rest? (Measured along the incline.)

Explanation / Answer

here,

mass of object, m = 13 kg
distance on horizonatl path, d = 7.4 m

coefficient of friction, uk = 0.31

Tension in rope, T = 60 N

From Work Energy Theoram,
When Pulling horizontally,

Work Done = Kinetic Energy
F*d*Cos0 = 0.5*m*v^2
60*7.4*Cos32 = 0.5* 13 * v^2

Solving for velocity, v = 7.61 m/s

From newton Second Law,SUM(F) = ma
mg*SinA + uk*mg*CosA - T = m*a

13 *9.81 *Sin32 + 0.31*13*9.81*Cos32 - 60 = 13a

upon solvign above eqn , a = 3.162

from Thrid eqn of motion, d = v^2/2a
d = 7.16^2/(2*3.162)
d = 8.107 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.