Could someone clearly explain step by step how to solve these? Studying for an e

Question

Could someone clearly explain step by step how to solve these? Studying for an exam. Thank you! (1) In Diagram 1, M is sliding (without friction) down the slope and pulling m upwards. Show that when you eliminate the tension T, you get the equation: (M+ m)a-Mg sin -mg. Next, find the system's acceleration a if M = 3m and the angle is 30°. Then, if the system is released from rest with m on the floor, use kinematics to calculate how much time m will take to be lifted to a height of 0.75 m. What will be the speed of the system when m reaches this height? (Remember that the system's acceleration is a.) a4ram

Explanation / Answer

(a)(M+m)*a = M*g*sin(theta)-m*g, M=3*m, theta= 30 degres. Given.

Hence,

(3*m+m)*a = 3m*g*sin(30)-m*g

4*a=3*g*sin(30)-g

Hence,

a = [3*g*sin(30)-g]/4

a =  [3*9.81*sin(30)-9.81]/4

=1.226 m/s^2

(b)

d = h/sin(theta) = 0.75/ sin(30) (since sin(theta) = h/d)

=1.5 m

d = v0*t +1/2*a*t^2

1.5 = 0*t +1/2*1.226*t^2

3/1.226 = t^2

t = 1.546 s.

v = v0 +a*t = 1.226*1.546

=1.8953 m/s

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