Why Are My Mechanics Problem Solutions Incorrect?

[DigitalSpark]

Hi,

I'm not getting some mechanics questions. I'm sure that I'm right... but the answer in the back of the book is different. I'll type it out for you guys

First Question:

"A body of mass 2kg is held in limiting equilibrium on a rough plane inclined at 20 degrees to the horizontal by a horizontal force X. The coefficient of friction between the body and the plane is 0.2. Modelling the body as a particle find X when the body is on the point of slipping:

a) up the plane.
b) down the plane."

I done a, but got it wrong, so I left out b, since I'm assuming I'm missing something.

I got 11.05 N, but the answer says 11.9N

The Second question is:

"Given that the resistances total 400N find the magnitude of the constant force needed to accelerate a car of mass 800kg from rest to 20m/s in 15 seconds."

Okay so I work out a, which is a=(v-u)/t=20/15=4/3

So F=ma=800x4/3=1066.67N

F+Resistance=Total Force=1466.77N, but the answer is 1470N apparently?? I'm confused.

Would like this to be resolved as soon as possible cos I've got a lot of mechanics questions to do.

Thanks :)

 

[Doc Al]

For the first problem: Show your work not just your answer.

For the second: They just rounded off to a reasonable number of significant figures; your answer matches.

 

[DigitalSpark]

Okay going to be a bit difficult as you need a force diagram. But just imagine a box on an inclined plane 20 degrees to the horizontal, with mg acting down, Normal Reaction and Frictional Force.

Normal Reaction=19.6Cos20=18.4N

Therefore Frictional Force=18.4x0.2=3.68N

So Xcos20=3.68+19.6sin20

X=11.05N

And the answer in the back of the book is 11.9N??

 

[Doc Al]

Normal Reaction=19.6Cos20=18.4N

Careful. Since the applied force is horizontal, it affects the normal force.

 

[DigitalSpark]

Careful. Since the applied force is horizontal, it affects the normal force.

Okay... how do I take that into account?? I don't know X in the first place? Give me a hint please :)

 

[Doc Al]

Find the normal force (in terms of X) by analyzing the force components perpendicular to the incline surface.

 

[DigitalSpark]

Find the normal force (in terms of X) by analyzing the force components perpendicular to the incline surface.

Thanks for your help.