a 330 kg piano slides 3.6 m down a 28 degree incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. the effective coefficient of kinetic froction is 0.4. calculate

a) the force exerted by the man,
b)the work done by the man on the piano
c)the work done by the friction force
d) the work done by the force of gravity, and
e) the net work done on the piano.

a.) the force exerted by the man is found by doing:

Fnormal= mass(gravity)(sin30) - u(mass)(gravity)(cos30)

...the u is the coefficient of friction.

b.) the work done by the man is found by using the force we found in the question above and putting it into:

W=Fd
My coeffiecent of friction was 0.40 so my total force was 421.5N

I just put it into W=421.5N(whateverdistanceIgiven)
for example is it was 9cm: (9cm = 0.09m)

W=421.5(0.09m) = 37.935J

c.) the work done by the friction force is solved the exact same way:
Since my coefficient of friction = 0.40 my Force of Friction = 0.41(280kg)(9.8m/s2)(cos30) = 950.5N

Then:
W=Fd = 950.5N(0.09m) = 85.545J

d.)the work done by gravity:
first find force of gravity by: mass(gravity)(sin30) = 1372N

then just plug into W=Fd = 1372(0.09m) = 123.48J

e.) the net work done on the piano = zero

I'm not sure if you noticed but the work of gravity minus the work of friction also gives you the work of the man!!

See: 123.48J - 85.545J = 37.935J !

Not sure if this was what your question was but... I remember doing this exact problem so I'm really hoping I was able to help you!!

-mayn zalik (not my real name :P...just a name I like)

Oh, and I'm sorry that I used different numbers. I copied and pasted my solution from my documents on my computer and these were my numbers. Just plug in your own numbers and get the answers :)

Once again, I'm really sorry BUT all the work is there!!

my numbers were:

280Kg
30degrees
0.40
and then gravity which is always the same on earth :)

oh and 9cm which is 0.09m

Thank you so much *zayn malik*

a.The mass of the piano is: .

It slides down for 3.6 meters.

The angle of inclination is: .

The effective coefficient of kinetic friction is: .

a)

The normal reaction is equal to,

For the x direction, the force equation will be,





.

So, the force exerted by the person is: 375.92 N.

a) Oh boy, the man must be as strong as Hercules to stop that piano! To find the force exerted by the man, we first need to calculate the force component of gravity parallel to the incline. Using some trigonometry magic, we find that the force component is given by F = m * g * sin(theta), where m is the mass of the piano (330 kg), g is the acceleration due to gravity (9.8 m/s²), and theta is the angle of the incline (28 degrees). Plug in the values, do the math, and you'll find the force exerted by the man.

b) The work done by the man on the piano can be calculated using the formula W = F * d, where W is the work done, F is the force exerted by the man, and d is the displacement of the piano (3.6 m). Plug in the values and do some multiplication, and you'll find the work done.

c) The work done by the friction force can be calculated using the formula W = F * d, where W is the work done, F is the frictional force, and d is the displacement of the piano (3.6 m). The frictional force can be found using the formula F = μ * N, where μ is the coefficient of friction (0.4) and N is the normal force. The normal force can be calculated using N = m * g * cos(theta), where m is the mass of the piano (330 kg), g is the acceleration due to gravity (9.8 m/s²), and theta is the angle of the incline (28 degrees). Plug in the values for the frictional force and displacement, and do the multiplication to find the work done.

d) The work done by the force of gravity can be calculated using the formula W = F * d, where W is the work done, F is the force of gravity, and d is the displacement of the piano (3.6 m). The force of gravity can be calculated using the formula F = m * g, where m is the mass of the piano (330 kg) and g is the acceleration due to gravity (9.8 m/s²). Plug in the values for the force of gravity and displacement, and do the multiplication to find the work done.

e) The net work done on the piano can be calculated as the sum of the work done by the man, the work done by the friction force, and the work done by the force of gravity. Add up all the work values and you'll find the net work done.

Now, go forth and conquer those calculations! Just remember to bring a clown nose for good luck.

To solve this problem, we need to consider the forces acting on the piano and use the relevant formulas. Let's break down each part of the problem step by step.

a) The force exerted by the man:
Since the man is pushing back on the piano parallel to the incline, the force exerted by the man will oppose the force of friction. We can calculate this force using the formula:

Force = mass * acceleration

In this case, the acceleration is zero since the piano is not accelerating. Therefore, the force exerted by the man is given by:

Force = mass * 0
Force = 0 Newtons

So the force exerted by the man is zero.

b) The work done by the man on the piano:
The formula to calculate work is given by:

Work = Force * distance * cos(theta)

In this case, the force exerted by the man is zero (as calculated in part (a)), so the work done by the man on the piano is also zero.

c) The work done by the friction force:
The formula to calculate the work done by friction is given by:

Work = Force of friction * distance * cos(theta)

The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

The normal force is the force perpendicular to the incline. In this case, the weight of the piano is acting vertically downwards and can be broken down into two components:

Normal force = weight * cos(theta)

Therefore, the force of friction is calculated as:

Force of friction = coefficient of friction * weight * cos(theta)

Now, we can calculate the work done by the friction force using the formula mentioned earlier.

d) The work done by the force of gravity:
The force of gravity acting on the piano can be calculated using the formula:

Force of gravity = mass * acceleration due to gravity

Since the piano is sliding down the inclined plane, we need to consider the component of gravity acting parallel to the incline. This component is given by:

Force of gravity parallel to incline = weight * sin(theta)

Therefore, the work done by the force of gravity is:

Work = Force of gravity parallel to incline * distance * cos(theta)

e) The net work done on the piano:
The net work done on the piano is the sum of the work done by all the forces acting on it. Therefore, the net work is:

Net Work = Work done by the man + Work done by the friction force + Work done by the force of gravity

Now, using the given values of the mass (330 kg), distance (3.6 m), incline angle (28 degrees), and coefficient of friction (0.4), you can substitute the values into the respective formulas to find the answers.

my numbers were:

280Kg
30degrees
0.40
and then gravity which is always the same on earth :)