2. A 260 kg piano is pulled up a frictionless 13 m plank to get it through French doors that are located 5.0 m above the ground.
a.
How much GPE (relative to the ground) does the piano have when it is inside the French doors?
b.
How much force is needed?
c.
How much force would be necessary to slowly lift the piano straight up?

Explanation:

a. GPE = mgh which is mass times gravity times height. For us, this is

GPE = 260(9.8)(5.0) so

GPE = 13000 J rounded to 2 sig fig's

b. is a little bit more involved, since we are on an incline. The formula for this is usually

where f is the pull of friction on the object. But we have no friction here, so f = 0. That means that we need to find the angle of inclination using right triangle trig. We have the height as 5.0 m and we have the length of the ramp as 13 m, so we an find the angle using the inverse sin button on our calculator.

so

degrees, rounded to 2 sig fig's as needed.

The formula to find Force is F = ma, which means we need the acceleration found in the equation

. Filling in:

weight = 9.8(260) = 2500 N so

2500sin23 = 260a and

a = 3.8 m/sec². Now we can find force:

F = 260(3.8) so

F = 990N

c. To life the piano straight up, we just need to overcome the pull of gravity along with the mass of the piano and the angle at which it is sitting. That has a formula of

Normal force = weight = wcosθ so

Normal force = 2500cos23 and

Normal force = 2300N

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form