Question

A time-varying net force acting on a 4.7 kg particle causes the object to have a displacement given by

x = a + b t + d t²+ e t³,

where a = 0.83 m , b = 2.6 m/s, d = −3.4 m/s², and e = 1 m/s³, with x in meters and t in seconds.

Find the work done on the particle in the first 2.7 s of motion.

Answer 1

any idea? @gerryliyana

Answer 2

@Algebraic!

Answer 3

x = a + b t + d t²+ e t³,

v =dx/dt = b + 2dt + 3et^2
a = dv/dt = 2d + 6et
a = 2(-3.4) + 6 (1) (2.7)
a = -6.8 + 16.2
a = 9.4

F = m a
F = (4.7) 9.4
F = 44.18 N

W = F x
W = 44.18 (a + b t + d t²+ e t³)

Answer 4

W = 44.18 x (0.83 +(2.6 x 2.7) + (-3.4 x 2.7^2) + (1 x 2.7^3)

Answer 5

W = 44.18 x 2.747
W =121.36 J

Answer 6

@geerky42 this my idea

Answer 7

dx = (b+ 2dt +3et^2) dt
F = ma = m*(2d+6et)
integrate: m*(2d+6et) *(b+ 2dt +3et^2) dt
from t=0..2.7

Answer 8

i don't see what's wrong with your work, but your answer is incorrect.

Answer 9

thanks, @gerryliyana and @Algebraic!

Answer 10

try the count returned by you in the same way
welcome

Answer 11

Maybe I made a mistake in the calculation

Answer 12

@Algebraic! integrate: " m*(2d+6et) *(b+ 2dt +3et^2) dt"

why (b+ 2dt +3et^2)? I though we only have to integrate the force itself?

F = m(2ct + 3et²), right?

Answer 13

F*dx

Answer 14

and F is ma ... what's a?

Answer 15

not (2ct +3et^2) ...

Answer 16

well, W = Fx

i have to integrate x too?

it is 2c + 6et

m(2ct +3et^2) is integral of force, wrong expression, my bad

Answer 17

no. W = integral(F*dx)

Answer 18

(assume c = d)

I wrote the different way. sorry for confusion -_-

Answer 19

you're not given F in terms of x though...

Answer 20

so you have to 'fix' that... by expressing everything in terms of t

Answer 21

(2d+6et) is acceleration

Answer 22

so F = m(2d + 6et)

Answer 23

yes

Answer 24

so i have to integrate force in respect to x? if no, why dx?

Answer 25

'normally' you do... but you can't here... at least not directly.
but you can write F(x) in terms of t, and dx in terms of t...

Answer 26

and then integrate that over the time interval

Answer 27

Is this going over your head? what class is this problem from?

Answer 28

calc. based physics I hope..?

Answer 29

ohh, i see. i got it now.

thanks.

Answer 30

sure:) hope it helped..

Answer 31

it's clear and it does help me
again, thanks.

Answer 32

great!