Originally posted by tomtom232heres another one
A 0.500 kg mass on a 3.20 meter string moves 2.5 radians/sec (1 revolution = 2 x pie x radians) in a horizontal circle. What angle does the string make with the vertical?
A sled weighing 200N rests on a 15 degree incline, held in place by static friction. The coefficient of static friction is 0.5. (a) What is the magnitude of the normal force on the sled? (b) Whatis the magnitude of the static friction on the sled? (c) The sled is now pulled up the incline at a constant speed by a child. The child weighs 500N and pulls on the rope with a constant force of 100N. The rope makes an angle of 30 degrees with the incline and has negligible weight. What is the magnitude of the kinetic fricition force on the sled? (d) What is the coefficient of kinetic friction between the sled and the incline?
first question is simple conical pendulum stuff:
let tension=T, weight = mg, angular velocity = w, length of string l, angle x.
resolve forces vertically:
Tcos[x] = mg
horizontally:
Tsin[x] = m(w^2) x lsin[x]
so T = m(w^2)l
subsituting into the first equation:
cos[x] = g/(w^2)l
and so x = 1.1, about 61 degrees.
Originally posted by etotheipiI agree, but x here is the angle the rope makes with the vertical. The "dip" is the additive inverse, 90 - 61 = 29 degrees.
first question is simple conical pendulum stuff:
let tension=T, weight = mg, angular velocity = w, length of string l, angle x.
resolve forces vertically:
Tcos[x] = mg
horizontally:
Tsin[x] = m(w^2) x lsin[x]
so T = m(w^2)l
subsituting into the first equation:
cos[x] = g/(w^2)l
and so x = 1.1, about 61 degrees.
for the second one:
let normal reaction force = R, frictional force up plane = F, coeff. of friction = m.
a)
resolving parallel to the plane:
R = 200cos[15] = 193N
b)
limiting equilibrium implies F = mR
so F = 97N
c)
the frictional force now acts down the plane, so
resolving along the plane:
F = 100cos[30] = 87N
d)
resolving parallel to the plane:
R + 100sin[30] = 200
so R = 150N
limiting equilibrium implies F = mR
so m = 0.58
Last part im not so sure about -- can you use limiting equilibrium in this case??
Wow, ignore my parts c and d from above as I have ignored a force 😲
c)
frictional force now acts down the plane
resolving along plane:
F + 200sin[15] = 100cos[30]
so F = 35N
d)
resolving parallel to the plane:
R + 100sin[30] = 200cos[15]
so R = 143N
limiting equilibrium implies F = mR
so m = 0.24
I hope 🙂