The 45-kg crate is pulled up the inclined surface by the winch. The coefficient of kinetic friction between the crate and the surface is The moment of inertia of the drum on which the cable is being wound is The crate starts from rest, and the motor exerts a constant couple on the drum. Use the principle of work and energy to determine the magnitude of the velocity of the crate when it has moved 1 m.

v = 0.384 m/s

Explanation:

The complete problem is as follows:

" The 45-kg crate is pulled up the  inclined surface by the winch. The coefficient of kinetic  friction between the crate and the surface is µk = 0.4.

The moment of inertia of the drum on which the cable is  being wound is IA = 4 kg-m2

.The crate starts from rest,  and the motor exerts a constant couple M = 50 N-m  on the drum. Use the principle of work and energy to

determine the magnitude of the velocity of the crate  when it has moved 1 m "

Given:

- The mass of the crate m = 45 kg

- Coefficient of kinetic  friction µk = 0.4

- Moment of inertia of the drum IA = 4 kg-m2

- Motor constant couple M = 50 N-m

- Motor Couple moment arm R = 0.15 m

- (The missing figure is attached)

Find:

Use the principle of work and energy to

determine the magnitude of the velocity of the crate  when it has moved 1 m

Solution:

Develop a FBD of the system consisting of Motor, rope and crate. (Attachment)

   The motor generates a couple M which induces a tension in the string depending on the amount of rotation proportional to the distance moved by the block.

   The crate experiences 3 forces: Normal contact force (N) exerted by the inclined surface on the crate. The Weight (W) of the crate acting vertically downwards and Friction Force (Ff = uk*N) along the surface contact parallel to slope while opposing uphill motion. ( See Attachment )

- Apply Equilibrium condition on the crate perpendicular to the slope:

                       N - m*g*cos(20) = 0

                       N = m*g*cos(20)

- For motion of the crate as it moves 1 m along the surface the work done is given by U_12:

            U_12 = Work done by motor couple - Work done against gravity - Work done by friction

            U_12 = M*θ - m*g*sin(20) - uk*N

Where,    θ is the angle of rotation of motor through distance of 1 m = 1 / R.

            U_12 = M/R - [m*g*sin(20) - uk*m*g*cos(20)]*(1)

- The kinetic energy of system at initial condition is zero ( T_1 = 0 ). The final state Kinetic energy are as follows T_2:

            T_2 = 0.5*m*v^2 + 0.5*IA*w^2

Where,

            w = v / R  ..... Angular speed at which the motor disc rotates.(No slip)

            T_2 = 0.5*m*v^2 + 0.5*IA*v^2 / R^2

            T_2 = v^2*( 0.5*m + 0.5*IA / R^2 )

- The Total Energy balance would be:

            T_1 + U_12 = T_2

            0 + M/R - m*g*sin(20) - uk*m*g*cos(20) = v^2*( 0.5*m + 0.5*IA / R^2 )

            v^2 =[ M/R - m*g*sin(20) - uk*m*g*cos(20) ] / [ ( 0.5*m + 0.5*IA / R^2 )]

- Plug in values:

            v^2 =[ 50/0.15 - 45*9.81*sin(20) - 0.4*45*9.81*cos(20) ] / [ ( 0.5*45 + 0.5*4 / 0.15^2 )]

            v = sqrt (0.147456)

            v = 0.384 m/s

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40