Acceleration of a mass down a decline (tricky)

[saltyload]

The plane is inclined at a 30 degree angle. The coefficient of kinetic friction between the mass and the plane is 0.1. The mass is 100kg. If the mass is moving up the inclined plane at a velocity of 2m/s, what tension should be applied to the rope in order to make the mass reverse directions in exactly 1 sec?



mgsin(theta)
mgcos(theta)
F_k = coefficient x mgcos(theta)
V = V_i + at



V = Vi + at a = 4m/s^2
Equation I used to solve:
ma = mgsin(theta) - T - F_k(theta)

My answer was 187N, actual answer is 387N. No idea how I can manipulate the equation to get 200N more.

 

[supratim1]

can you provide a diagram to make it clear?

 

[saltyload]

can you provide a diagram to make it clear?

Found this on google. The diagram in the book is identical, just ignore the hanging mass. I need to find the tension in the rope.

 

[lswtech]

First, to make it reverse direction, required retardation, along the inclined plane is 2
0.1 mg cos30 +mg sin30 - T = 2m

Seems the key here is "make the mass reverse directions" , it just means "make the mass to have 0 velocity in 1 sec" but not "make the mass to have -2 in 1 sec"

 

[SammyS]

I believe your acceleration is wrong. It should be 2 m/s² and in the direction opposite it initial velocity. The velocity has to go from 2 m/s to 0 m/sin a time of 1 s.

 

[saltyload]

First, to make it reverse direction, required retardation, along the inclined plane is 2
0.1 mg cos30 +mg sin30 - T = 2m

Seems the key here is "make the mass reverse directions" , it just means "make the mass to have 0 velocity in 1 sec" but not "make the mass to have -2 in 1 sec"

what is 2m?

edit:
I got the 387N by using your equation, but changed the positions of T and 2m. Can you explain the logic behind your equation. I sort of get it, but I need some clarification.

I understand the force of friction and the downward force of the mass are added because they act in the same direction. And T is in the opposite direction, but how do you explain the 2m?

 

[lswtech]

The question stated " make the mass reverse directions in exactly 1 sec" and I thought the retardation should be 2ms^-2 but not 4.

and the 2m means m*a and putting a = 2

Since the direction of retardation is pointing towards the ground, and the Net force in this direction is Friction + Weight component - Tension and the Net acceleration is 2

 

[saltyload]

The question stated " make the mass reverse directions in exactly 1 sec" and I thought the retardation should be 2ms^-2 but not 4.

and the 2m means m*a and putting a = 2

Since the direction of retardation is pointing towards the ground, and the Net force in this direction is Friction + Weight component - Tension and the Net acceleration is 2

So is the acceleration (ma) in the same direction of the Tension?

 

[lswtech]

No. Reverse

(Weight pulls down the block and it is the origin of the acceleration downward)