An air puck of mass m_1 = 0.33 kg is tied to a string and allowed to revolve in

Question

An air puck of mass m_1 = 0.33 kg is tied to a string and allowed to revolve in a circle of radius R = 0.9 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m_2 = 1.0 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? N (b) What is the horizontal force acting on the puck? N (c) What is the speed of the puck? m/s A roller coaster vehicle has a mass of 500 kg when fully loaded with passengers (see figure). (a) If the vehicle has a speed of 22.0 m/s at point, what is the force of the track on the vehicle at this point? N (b) what is the maximum speed the vehicle can have at point in order for gravity to hold it on the track? m/s

Explanation / Answer

1)

m1 = 0.33 kg

R = 0.9 m

m2 = 1 kg

a) tension in the string is T = m2 * g = 1 * 9.8 = 9.8 N

T = 9.8 N

b) the horizontal force is same tension so

F = 9.8 N

c) from the relation

Fc = T

m1 * v^2 / R = 9.8

0.33 * v^2 / 0.9 = 9.8

v = 5.17 m/s

2)

Given m = 580 kg

a) v = 22 m/s

at point A the normal force is balanced by the centripetal force and weight so

n = (m * v^2 / r) + ( m * g)

n = (580 * 22^2 / 10) + (580 * 9.8)

n = 33756 N

b)

here m * v^2 / r = m * g

v^2 /r = g

v^2 / 15 = 9.8

v = 12.12 m/s

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