Written homework to be turned in at the beginning of the first studio in week 10

Question

Written homework to be turned in at the beginning of the first studio in week 10. Consider the two situations sketched below. In the first a machine must pull a box up a rough slope at constant speed. The mass of the box is M = 800 kg, the coefficient of kinetic friction is mu k = 0.2, and the slope is inclined at 15 degree to the horizontal. In the second situation the machine must pull an equally massive wheel up the same slope. The cable is attached to the axle of the wheel and exerts negligible torque about that axis. If both the box and the wheel move up the slope at 0.5 m/s then how much power (in Watts) must the machine supply for each task?

Explanation / Answer

hi

you need to know that power P=F*v (where F is Force od machine and v is velocity of box or wheel)

in 1-st.& 2-nd situation you have to subdivide box weight on components paralel and perpendicular to slope.(see link)

http://tinypic.com/r/35ivf68/5

1-st

now you have 2 forces directed down the slope. Wx is x component of weight(m*g) (paralel to slope).

form trigonometry you have that Wx=W*sin(15)=m*g*sin(15)

other force if friction and Ff=N* (N reaction of surface and is coef. of kinetic friction)

again from N=W*cos(15)=m*g*cos(15) => Ff=*m*g*cos(15)

velocity is constant so sum of all forces alonge path movemant is 0 for that we get that Fm (force of machine) Fm=Wx+Ff

whan you find Fm insert it in P=Fm*v and you get result.

2-nd situation is similar EXCEPT that there is on KINETIC friction for rotation. than Fm=Wx. you can use Wx form first part because it's same slope and mass of object. and you get that power P=Wx*v

hope i helped you and sorry for bad engslih. !! :)

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