MasteringPhysics Chapter 12- Google Chrome https://session.masteringphysics.com/

Question

MasteringPhysics Chapter 12- Google Chrome https://session.masteringphysics.com/myct/itemView?assignmentProblemiD-56100031 hys201-2016-Spring bapter 12 Problem 12 69 previous9 o 15 ne Problem 12.69 Part A The two blocks in the figure Eigure 1) are connected by a massless rope that passes over a puilley The pulley is If the blocks are released from rest, how long does it take the 4 0 kg block to reach the floor? 17 cm in dameter and has a mass of 2 5 kg As the pulley tums, friction at the axle exerts a torque of magnitude 0 48 N-m Express your answer to two significant figures and include the appropriate units. 1.3 My Answers Gve U Incorrect; Try Again; 3 attempts remaining 4.0kg 10 m 20kg

Explanation / Answer

Let:
m1 be the left hand mass,
T1 be the left hand tension,
m2 be the right hand mass,
T2 be the right hand tension,
g be the acceleration due to gravity,
a be the acceleration of the masses,
alpha be the angular acceleration of the pulley,
r be the radius of the pulley (assumed solid),
F be the friction couple,
h be the descent for m1,
t be the time taken.

For mass m1:
m1 g - T1 = m1 a
T1 = m1(g - a)

For mass m2:
T2 - m2 g = m2 a
T2 = m2(g + a)

For the pulley:
(T1 - T2)r - F = I alpha
= (m3 r^2 / 2)(a / r)

T1 - T2 = F / r + m3 a / 2

Eliminating T1 and T2:
m1(g - a) - m2(g + a) = F / r + m3 a / 2

(m1 - m2)g - (m1 + m2)a - m3 a / 2 - F / r
(m1 + m2 + m3 / 2)a = F / r + (m1 - m2)g
a = [ F / r + (m1 - m2)g ] / (m1 + m2 + m3 / 2)

h = at^2 / 2
t = sqrt(2h / a)
= sqrt{ h(2m1 + 2m2 + m3) / [ F / r + (m1 - m2)g ] }

t = sqrt{ 1( 2 * 4 + 2 * 2 + 2.5) / [ 0.48 / 0.085 + (4 - 2)9.81 ] }
= 0.76 sec.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---