An amusement park ride called The Swing consists of a chair hanging from a 4.5 m

Question

An amusement park ride called The Swing consists of a chair hanging from a 4.5 m long chain. The top of the chain is attached to a rotating spindle. When the ride is in motion, the chair moves in a horizontal circle and the chain makes an angle of 25.0degree with the vertical (see diagram). If a rider experiences a radial acceleration of 3g what is the ride's period? In the diagram at right, M_1 5.55 kg. M_2 = 2.33 kg. What is the minimum coefficient of static friction mu such that the system is in equilibrium? What is the maximum value for M_2 so that equilibrium is still possible? A car of mass M goes around an unbanked curve of radius R. Find the maximum velocity the car can have and still stay on the road. In the diagram at right, a mass M = 17.5 kg is hanging from two cables as shown. Find the tension in each cable. theta = 35.0degree, phi = 44.0degree A 1.75 kg ball is attached to 2 identical rubber bands, as shown. The rubber bands are attached to a wall. When you let go of the ball, it will sag down. What angle will the rubber bands make with the horizontal? (Find in terms of T. the tension in each rubber band)

Explanation / Answer

after Drawing FBD,

we get

T1 cos theta = T2 cos phi

so T1 cos 35 = T2 cos 44

T1 *0.819 = 0.719 * T2

T1 = 0.877 T2 -----------------1

also

T1 sin theta + T2 sin phi = mg

T1 sin 35 + T2 sin 45 = (17.5 * 9.81)

0.573 T1 + 0.707 T2 = 171.675

from 1

0.877 * 0.573 T2 + 0.707 T2 = 171.675

T2 = 142 N (ANSwer)

so T1 = 0.877 * 1420.87*1420.877

T1 = 124.534 N (ANSWER)

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