Question

Two blocks (with masses 20.5 kg and 68 kg)
are connected by a string as shown. The pulley is frictionless and of negligible mass. The
coefficient of kinetic friction between block
and machine is 0.257.

Find the change in the kinetic energy of the
block on the incline as it moves a distance of
15.4 m up the incline if the system starts from
rest.

Answer 1

Knowing that W = d∑F = ΔKE, should I find the sum of force or what?

Answer 2

find out the work done by each individual forces separately

Answer 3

Well, we don't know tension, so how can we deal with it? I think can solve this by finding acceleration then use ΔKE = mad.

Answer 4

since work done is a scalar quantity, so it can be added algebraically.

Answer 5

there is another way also , where u wont have to use work-energy theorem

Answer 6

Oh, so i have to set the equation of work done by each of the object then combine them?

Answer 7

wait...

Answer 8

1st write down the equations of motion for both blocks then find the acceleration of the block.

Answer 9

then use kinematic equation v^2-u^2= 2 a x

Answer 10

Isn't thats what I said? finding acceleration, right? and why kinematic equation?

Answer 11

so u can find v from the above equation...hence chage in the kinetic energy

Answer 12

We don't know initial and final velocity.

Answer 13

system starts from rest so u=0

Answer 14

u will get acceleration from the equations summation F= ma

Answer 15

Oh, right. So find acceleration then use this equation W = ΔKE = mad?

Answer 16

u know x

Answer 17

to find final answer?

Yes i know x.

Answer 18

15.4 m, right?

Answer 19

yes

Answer 20

So first i have to find the acceleration then use this equation W = ΔKE = mad to find the answer im looking for, right?

Answer 21

max*

Answer 22

but anyhow u'll have to use F=ma because u dont know the tension in d string

Answer 23

by d, i mean displacement. (x = d) sorry for confusion.

Answer 24

then either u use kinematic equation v^2- u^2= 2ax or work energy theorem.

Answer 25

it's okay

Answer 26

I think my way is much easier. are there something wrong with my way?

Answer 27

see i can derive the work energy theorem from v^2- u^2=2ad

Answer 28

Both blocks have same acceleration, all i have to do is find acceleration then multiply it by mass of block on inclined plane and displacement.

Answer 29

isn't thats right?

Answer 30

Im doing it your way. I got v = 13.167 m/s

then use 1/2 mv²f - 1/2 mv²o

From that, I got 1776.961 J

right?

Answer 31

And in my way, i got same answer. it seems it has two ways to find the solution... Thank for your time, i appreciate it.

Answer 32

:)
sorry, there was some problem with my internet connection.

Answer 33

see i can derive the work energy theorem from v^2- u^2=2ad
multiply both sides by m/2
then u have change in the kinetic energy on LHS

Answer 34

RHS= m a d

Answer 35

ma= net force on the block

Answer 36

so mad= work done by all the forces

Answer 37

so there is no surprise that by both way u'll get d same answers.

Answer 38

I see. thanks.

Answer 39

:)