Dynamics

[d0minicz]

anyone x]

[Mao]

1. A body mass of M kg is pulled along a rough horizontal plane (coefficient of friction ) by a constant force of F newtons, at an inclination of . Find the acceleration of the body if:

a) is upwards from the horizontal

b) is downwards from the horizontal.

In the verticle direction:


In the horizontal direction:

2. A particle of mass 5kg is being pulled up a slope inclined at to the horizontal. The pulling force, F newtons, acts parallel to the slope, as does the resistance with a magnitude of one-fifth of the magnitude of the normal reaction.

a) Find the value of F, such that the acceleration is up the slope.

b) Also find the magnitude of the acceleration if this pulling force now acts at an angle of to the slope (ie. at to the horizontal).

a)
Perpendicular to slope:

Parallel to slope:


b) Draw a picture to help:
Perpendicular to slope:

Parallel to slope:


There may have been calculation errors

[d0minicz]

1. The diagram shows a smooth plane inclined at an angle of to the horizontal. At the top of the plane there is a smooth pulley over which passes a taut, light string. On the end of the string is attached a block of mass 5kg lying on the plane. The other end is attached to a block of mass M kg hanging down vertically. If the mass of M kg is moving downwards with an acceleration of find:
a) M
b) the tension in the string

2. The diagram shows a particle of mass 4kg on a smooth horizontal table. The particle is connected by a light inelastic string which passes over a smooth pulley to a particle of mass 8kg which hangs vertically. Find:
a) the acceleration of the system
b) the tension in the string

Please helpppppp =]

thanks

[ed_saifa]

It has been a while but I think they're right

[d0minicz]

indeed you got em right ... damn answers were staring at me lol missed them
thanks man

[d0minicz]

Sighhh another :

1. In the situation shown in the diagram, what mass m kg is required in order to give the system an acceleration of ?

Do we take a = -0.8 m/s^2? confuseeed

thanks again

[ed_saifa]

No you keep it as postive
The M kg will move down. The 5kg mass will move to the right.

[d0minicz]

oh how do you know that the M kg will move down?

[ed_saifa]

Assumption i guess.

[d0minicz]

ah ok
so if you assumed the block M kg was moving up and the 5kg block was moving to the left, would it would be wrong

[ed_saifa]

I think they would tell you if the block was moving up. For these connected mass type questions, it's more logical for the mass to go down. But i guess you could do it twice, one for the mass dropping down, and one for it moving up.

[d0minicz]

1. A body of mass 10 units is accelerated from rest by a force F whose magnitude at time t is given by :

Find:
a) the speed of the body when t=10
b) the distance travelled in this time

thankssss

[enwiabe]

I'll guide you with this qu, dom (rather than give full soln).

Remember that F = m*a, and that the mass is constant.

So, acceleration, a, = F/m = (that hybrid function)/10

Integrate once to get velocity (i think you missed off the initial condition in the question stem, there should be something like "velocity is b metres per second when t = 0" or something to that effect.) That shouldn't trouble you at all to get the velocity for the first part, (just integrate from 0 to 10), but for the 2nd part you'll need to integrate again and so you'll need to know what the initial velocity condition was.

So yeah, for b), integrate again to get the distance.

[kamil9876]

you need to split this up into two parts; t between 0 and 5 and t beyond 5.




but c=0 since v(0)=0 (starting from rest)




Now for :





however




now you can easily find v(10) from here on.

hopefully no stupid mistakes but you can get the idea.

[enwiabe]

... reading kamil's post, I am going to smack myself on the head for not reading the question properly, and for missing the initial condition . >_>