Please show work. And, thank you in advance for the help. A Block of mass mA = 2
ID: 2243517 • Letter: P
Question
Please show work. And, thank you in advance for the help.
A Block of mass mA = 2.0 kg rests on a ramp with which it has a coefficient of friction = 0.3. The ramp is raised 30 degrees from the horizontal. A string attached to the block passes over a pulley and is attached to a block of mass mB = 6kg. The pulley has a mass of mP = 2.5 kg and a radius of 10 cm.
A. Draw a free body diagram for block A.
B. What is the moment of inertia, I, for the pulley?
C. Use newtons second law (for forces and torques) to find the acceleration of the two blocks.
D. If the system starts at rest and the block moves for 2.3 seconds, what will the angular velocity of the wheel be?
E. If you use a different ramp, what minimal coefficient of friction will keep the blocks stationary?
A Block of mass mA = 2.0 kg rests on a ramp with which it has a coefficient of friction = 0.3. The ramp is raised 30 degrees from the horizontal. A string attached to the block passes over a pulley and is attached to a block of mass mB = 6kg. The pulley has a mass of mP = 2.5 kg and a radius of 10 cm. Draw a free body diagram for block A. What is the moment of inertia, I, for the pulley? Use newtons second law (for forces and torques) to find the acceleration of the two blocks. If the system starts at rest and the block moves for 2.3 seconds, what will the angular velocity of the wheel be? If you use a different ramp, what minimal coefficient of friction will keep the blocks stationary?Explanation / Answer
b) pulley has I = 0.5*2.5*0.1*0.1 = 0.0125
c) let B moves down assume
6*9.8-T=6*a
T- (2*9.8*0.3*cos30) -(2*9.8*sin30)=2a
so adding
we get
a=5.488 m/s^2 m/s^2
c)
T = 25.92
T=I*alpha
25.92 =0.0125 *alpha
alpha= angular accelratoin = 2073.6
angula velocity= 4769.28 rad/sec
e) to find coeficient u
6*9.8-T= 0
T - (2*9.8*u*cos30)-(2*9.8*sin30)=0
u =2.88