Question

please help,,
Find acceleration of blocks ​

Answer 1

Answer:

sorry

Explanation:

Answer 2

Answer:

Explanation:

this can be solved  by multiple methods

first by system method

let acceleration of wedge = A

acceleration of block wrt to wedge = 3A

acceleration of block = A+3Acostheta i

summation fx = 3t+tcostheta

M(A)+m(A+3Acostheta) = 3t+tcostheta

analyzing block along incline

mgsintheta-t=m(3A+Acostheta)

t=mgsintheta-m(3A+Acostheta)

M(A)+m(A+3Acostheta) =(mgsintheta-m(3A+Acostheta))(3+costheta)

M(A)+m(A+3Acostheta) = 3mgsintheta+mgsinthetacostheta - 9mA-3mAcostheta-3mAcostheta-mAcos^2 theta

A(M+10m+9mcostheta+mcos^2 theta) = 3mgsintheta+mgsinthetacostheta

A=3mgsintheta+mgsinthetacostheta / M+10m+9mcostheta+mcos^2 theta)

3A=9mgcostheta+3mgsinthetacostheta / M+10m+9mcostheta+mcos^2 theta

above is acceleration wrt to incline

for wrt to ground put A in below equation

A+3Acostheta i -3Asintheta j

inertial method wrt to ground

applying equation for M

3t+tcostheta-nsintheta = MA

applying equation for m

mg-ncostheta = 3mAsintheta

nsintheta-tcostheta=m(3Acostheta+A)

by above

ncostheta = mg-3mAsintheta

n=mgsectheta-3mAtantheta

put this in 3rd equation of this method

mgtantheta-3mAtanthetasintheta-tcostheta = m(3Acostheta+A)

mgtantheta-3mAtanthetasintheta-3mAcostheta-mA = tcostheta

mgtanthetasectheta-3mAtan^2 theta -3mA-mAsectheta = t

place the above in equation 1 of this method

3t+tcostheta-nsintheta = MA

t(3+costheta)-nsintheta = MA

place the value of n and t you will get A

and for acceleration wrt to wedge = 3A

acceleration wrt to ground A+3Acostheta i -3Asintheta j

inertial method wrt to incline

applying equation for M

3t+tcostheta-nsintheta = MA

applying equation for m along the incline

mgsintheta-t=m(3A+Acostheta)

mgcostheta-n = m(Asintheta)

put values of t and n in above equation

you will get A

for acceleration wrt to wedge = 3A

acceleration wrt to ground = A+3Acostheta i -3Asintheta j

non inertial method wrt to ground

applying equation for M

3t+tcostheta-nsintheta = MA

applying equation for m

mg-ncostheta=3mAsintheta

nsintheta-tcostheta-mA = 3mAcostheta

solving you get A

and for acceleration wrt to ground = A+3Acostheta i -3Asintheta j

acceleration wrt to wedge = 3A

non inertial method wrt to incline

applying equation for M

3t+tcostheta-nsintheta = MA

applying equation for m

mgsintheta-t-mAcostheta = 3mA

mgcostheta+masintheta=n

put n and t in above equation

you will get same

for acceleration wrt to ground = A+3Acostheta i -3Asintheta j