Problem 3 (15 points): In the figure shown, a 10 kg block hangs on the right, an

Question

Problem 3 (15 points): In the figure shown, a 10 kg block hangs on the right, and a 4 kg block slides on a frictionless surface. The angle of the incline is 32°. The pulley is in the shape of a disk, with a mass of 5 kg, and a radius of 10 cm. The strings are ideal. The system is released from rest. ? m. 2 ? ) 32° Please answer each of the folowing questions. a) When the hanging mass has moved 10 cm, what is its velocity b) Wh en the hanging mass has a velocity of 1.2 m/s, what is the kinetic energy of the pulley' FT 2121 8 1 T 12-3129

Explanation / Answer

here,

accelration , a = net force /effective mass

a = ( m1 * g - m2 * g * sin(theta))/(m1 + m2 + 0.5 * m * r^2 /r^2)

a = ( 10 * 9.81 - 4 * 9.81 * sin(32)) /( 10 + 4 + 0.5 * 5) m/s^2

a = 4.7 m/s^2

a)

the velocity , v = sqrt(2*a*s)

v = sqrt(2 * 4.7 * 0.1)

v = 0.97 m/s

b)

for v = 1.2 m/s

the kinetic energy of pulley , KE = 0.5 * I * w^2

KE = 0.5 * ( 0.5 * m * r^2) * ( v/r)^2

KE = 0.5 * ( 0.5 * 5) * (1.2)^2 J

KE = 1.8 J

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