Show work! Partial credit cannot be given if no work or explanation is given. Ci

Question

Show work! Partial credit cannot be given if no work or explanation is given. Circle your final answer Make sure final answers are in the s, when appropriate correct significant figures and unit A mass m = 0.25 kg is attached to a light string of length L is displaced an angle 90° from the vertical and released at t = 0 s. At 30·"on the other side of the pendulum release point is a tationary block equal in mass to the pendulum, attached to a spring of constant k = 6.5 N/m on a frictionless, angled surface The mass-spring system is angled at 30°. When the pendulum collides with the block, the pendulum very quickly detaches from the string and sticks to the block (assume this happens instantaneously) · 1.0 m, making a simple pendulum. It L = 1.0 ml 30° 30° a. At what speed will the pendulum hit the block? The x-0.0 m position has been set at the spring no-stretch length. Given this mark, what is the furthest x-position (down the hill) that the block-pendulum system gets from x = 0.0 m. b.

Explanation / Answer

part c:as obtained in part b,

maximum distance achieved by block and pendulum system is 0.32 m

hence amplitude of the SHM=0.32 m

part D:

for the pendulum,angular frequency=w=sqrt(g/l)=3.1305 rad/sec

then time taken to cover (pi/2)+(pi/6)=2*pi/3 radians = angle/angular speed

=(2*pi/3)/3.1305=0.669 seconds

once the pendulum sticks with the block,it will compress the block till it reaches amplitude at the other end

at the time of striking the block, the block is in equilibrium.

hence if elongation of the spring is x,

then k*x=m*g*sin(30)

==>6.5*x=0.25*9.8*0.5

==>x=0.18846 m

hence to reach maximum compression, the block pendulum system will have to travel 0.18846+0.32=0.50846 m

time period of the blok-pendulum system=2*pi/sqrt(k/m)=2.46446 seconds

then equation of block -pendulum SHM=0.32*sin((2*pi/2.46446)*t+alpha)

at t=0, location=0.18846

==>sin(alpha)=0.18846/0.32=36.0816 degrees=0.62974 radians

hence equation of SHM:x(t)=0.32*sin(2.5495*t+0.62974) m

if time taken to reach -0.32 m is t1,

then -0.32=0.32*sin(2.5495*t+0.62974)

==>2.5495*t+0.62974=3*pi/2=4.71238

==>t=(4.71238-0.62974)/2.5495=1.60135 seconds

hence total time taken to reach first maximum compression=

=time taken by pendulum to travel (90+30=120 degrees)+ time taken by pendulum block system to reach x=-0.32 m

=0.669+1.60135=2.27035 seconds

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.