1.A marble rolls on the track shown in the figure below, with h B = 23 cm and h

Question

1.A marble rolls on the track shown in the figure below, with hB = 23 cm and hC = 12 cm. If the marble has a speed of 2.3 m/s at point A, what is its speed at points B and C?

vB =

vC =

2.A puck (mass m1 = 1.15 kg) slides on a frictionless table as shown in the figure below. The puck is tied to a string that runs through a hole in the table and is attached to a mass m2 =3.5 kg. The mass m2 is initially at a height of h = 3.5 m above the floor with the puck traveling in a circle of radius r = 0.92 m with a speed of 3.5 m/s. The force of gravity then causes mass m2 to move downward a distance 0.35 m.

a) What is the new speed of the puck?

(b) What is the change in the kinetic energy of the puck?

3.A child of mass 51 kg jumps onto the edge of a merry-go-round of mass 165 kg and radius 2.5 m that is initially at rest as sketched in the figure below. While in the air (during her jump), the child's linear velocity in the direction tangent to the edge of the merry-go-round is 11 m/s. What is the angular velocity of the merry-go-round plus child after the child jumps onto the merry-go-round?

5.A ball of mass 3.1 kg is tied to a string of length 1.8 m. The other end of the string is fastened to a ceiling, and the ball is set into circular motion as shown in the figure below. If ? =26

Explanation / Answer

1. 1/2 mv^2 = 1/2mv^2 + m g h

0.5*2.3^2 = 0.5*v^2 + 9.81*.23

vB= 0.882 m/s

0.5*2.3^2 = 0.5*v^2 + 9.81*.12

vC = 1.71 m/s

2. a)conservation of angular momentum

m v r = m v r

3.5*0.92 = v*(0.92-0.35)

v=5.65 m/s

b) dKE = 1/2 mv^2 - 1/2 mv^2 = 0.5*1.15*(5.65^2 - 3.5^2)= 11.31 J

3.
conservation of angular momentum
m v r = ( mr^2 + I) w
51*11*2.5 = (51*2.5^2 + 0.5*165*2.5^2)*w
w=1.68 rad/s

4) conservation of angular momentum
mv r = m v r
8.9E10*54 = 5.3E12*v
v = 8.9E10*54/5.3E12=0.907 km/s

5) sum forces in the y
T cos theta - mg = 0
T = mg/cos theta

sum in the x
T sin theta = mv^2/r
m g tan theta = mv^2/r
v = sqrt( gr tantheta)

L = m v r = 3.1*1.8*sin(26 degrees)*sqrt(9.81*1.8*sin(26 degrees)*tan(26 degrees))= 4.75

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