dynamics/kinematics questions

[kdgamz]

i cant seem to get my head around these two questions.. anyone?


Question1

A particle of mass 20 kg at rest is acted on by a force that decreases uniformly with the
distance travelled. The force is initially 100 N and 30 N after 20 metres. The speed of the
particle at this time is:

A 3√230 m/s
B 130 m/s
C 230 m/s
D √130 m/s
E 5√193 m/s

Question 2

An object of mass 10 kg is subjected to a variable force described by the expression
(100 − 2x) newtons, where x is the distance up a ramp that makes an angle of 10° with the
horizontal. Assume the ramp is smooth and that the object starts from rest from the bottom
of the ramp.
(a) Find the speed, correct to two decimal places, of the object
(i) 3 m up the ramp

thanks

[Flaming_Arrow]

is the answer D for q1?

[kdgamz]

yeh but how?

[Flaming_Arrow]

a= 5 when x=0     a=3/2 x=20

find the equation of acceleration in terms of x







we know that



so

[Flaming_Arrow]

whats the answer to 2a?

[Mao]

Question 2

An object of mass 10 kg is subjected to a variable force described by the expression
(100 − 2x) newtons, where x is the distance up a ramp that makes an angle of 10° with the
horizontal. Assume the ramp is smooth and that the object starts from rest from the bottom
of the ramp.
(a) Find the speed, correct to two decimal places, of the object
(i) 3 m up the ramp

I'm assuming the variable force points up the ramp

Then,

[kdgamz]

a= 5 when x=0     a=3/2 x=20

find the equation of acceleration in terms of x







we know that



so

nice wrk! thanks, my mistake was putting acceleration as 1.5 without even using the other 5...

[kdgamz]

Question 2

An object of mass 10 kg is subjected to a variable force described by the expression
(100 − 2x) newtons, where x is the distance up a ramp that makes an angle of 10° with the
horizontal. Assume the ramp is smooth and that the object starts from rest from the bottom
of the ramp.
(a) Find the speed, correct to two decimal places, of the object
(i) 3 m up the ramp

I'm assuming the variable force points up the ramp

Then,

thanks man (the answers 6.93 right?)

one more thing...i used

and got the same answer .. can i do this???
.. and also when im doin trig, when do i use DEGREE mode and when do i use RADIAN mode... in this case only DEGREE mode works

thanks

[Flaming_Arrow]

Question 2

An object of mass 10 kg is subjected to a variable force described by the expression
(100 − 2x) newtons, where x is the distance up a ramp that makes an angle of 10° with the
horizontal. Assume the ramp is smooth and that the object starts from rest from the bottom
of the ramp.
(a) Find the speed, correct to two decimal places, of the object
(i) 3 m up the ramp

I'm assuming the variable force points up the ramp

Then,

thanks man (the answers 6.93 right?)

one more thing...i used

and got the same answer .. can i do this???
.. and also when im doin trig, when do i use DEGREE mode and when do i use RADIAN mode... in this case only DEGREE mode works

thanks

look at what the angle is given in, in this case its in degrees so u have to use degrees, but you can convert it to radians and use radian mode if u want to

[kdgamz]

so the angle is 10 degrees therefore i use DEGREE mode... if the angle was π/6, then i would have to use RADIAN mode..right?

[Flaming_Arrow]

so the angle is 10 degrees therefore i use DEGREE mode... if the angle was π/6, then i would have to use RADIAN mode..right?

by n/6 if u mean pi/6 then yes

[kdgamz]

so the angle is 10 degrees therefore i use DEGREE mode... if the angle was π/6, then i would have to use RADIAN mode..right?

by n/6 if u mean pi/6 then yes

lol..yeh thats it, thanks man

[kdgamz]

one more.. its continued from question 2

Question 2

(b) What is the maximum distance the object can travel up the ramp?

The velocity function I got was v = √((20x)-0.2x^2- 2gxsin10), I found its derivative and made it equal to zero and solved for x,  i got 41.49 m, but the answer is double that: 82.98 m

thanks

[kdgamz]

maximum distance occurs when v=0 and not a=0, if they tell you to find the maximum velocity then ur way is right

yeh that gives the right answer..thanks 8-)

[Flaming_Arrow]

one more.. its continued from question 2

Question 2

(b) What is the maximum distance the object can travel up the ramp?

The velocity function I got was v = √((20x)-0.2x^2- 2gxsin10), I found its derivative and made it equal to zero and solved for x,  i got 41.49 m, but the answer is double that: 82.98 m

thanks

maximum distance occurs when v=0 and not a=0, if they tell you to find the maximum velocity then ur way is right

sorry accidently deleted my post