PLEASE SHOW FULL STEPS problem 1: 8. A ball of mass 0.3 kg at the end of a rigid
ID: 2263105 • Letter: P
Question
PLEASE SHOW FULL STEPS
problem 1: 8. A ball of mass 0.3 kg at the end of a rigid rod is undergoing circular motion in a circle of radius 0.5 m. The
angular motion of the ball is described by the function,
?=A+B t^2?C t^4
where
A=?/3 B = 3rad/s^2 C = 2rad/s^4
A) Find the angular speed (?) as a function of time.
B) Find the angular acceleration (?) as a function of time.
C) Find the net force on the ball at time t= 3 s.
problem 2:
A block of mass 1 kg is on a turntable 0.5 m from the center of the turntable. The turntable starts from rest
and has a constant angular acceleration of 0.2 rad/s^2. The coe?cient of static friction between the turntable and the block is 0.6.
A) Find the angular speed of the turntable as a function of time.
B) Find the radial and tangential components of the acceleration of the block as a function of time.
C) Find the radial and tangential components of the net force on the block as a function of time.
D) What is the maximum force that static friction can provide on the block?
E) When does the block start to slip?
F) How many rotations has the block gone through before it starts to slip?
problem 3: At what speed can a car round a curve banked at an angle of 8? and experience no frictional force if
the radius of curvature of the curve is 250 m?
Explanation / Answer
1)
A) W = 2*B*t - 4*C*t^3
B) alfa = 2*B - 12*C*t^2
C) at t= 4 W = 2*3*3 - 4*2*3^3 = ?54rad/s
alfa = 2*3 - (12*2*9) = ?210
Fr = M*R*W^2 = 0.3*0.5*54^2 = 437.4 N
Ft = M*a = M*R*alfa = 0.3*0.5*?210 = ?31.5 N
F = sqrt(Ft^2+Fr^2) = 438.53 N
2)
A) W = alfa*t = 0.2t
B) a_r = R*W^2 = 0.5*(0.2t)^2 = 0.5*0.2*0.2*t^2 = 0.02t^2
a_t = R*alfa = 0.5*0.2*t = 0.1t
C) Fr = M*R*W^2
Ft= M*a = M*R*alfa
D) f = mue*M*g = 0.6*1*9.8 = 5.88 N
E) Fr = f
M*R*W^2 = mue*M*g
W = (mue*g/R)^(1/2) = ((0.6*9.8)/0.5)^(1/2) = 3.429 rad/s
t = W/alfa = 3.429/0.2 = 17.145 s
F) theta = 0.5*alfa*t^2 = 0.5*0.2*17.145^2 = 29.395 rad = 4.68 rotations
3) tan8 = V^2/rg
V = 18.55 m/s