Newlyweds Allie (mass m1 m 1 = 62.8 kg) and Josh (mass m2 m 2 = 83.7 kg) are ini
ID: 1426195 • Letter: N
Question
Newlyweds Allie (mass m1 m 1 = 62.8 kg) and Josh (mass m2 m 2 = 83.7 kg) are initially standing still at opposite ends of a plank of length L = 4.9 m and mass M = 20.6 kg, with Allie at the left end and Josh at the right end. The plank is initially at rest on smooth ice (a frictionless horizontal surface).
1)Suppose they walk toward each other and meet for a kiss at the exact center of the plank. What is the displacement of the plank from its initial position as they are kissing? (The +x direction is toward the right in the picture).
a..31 m
b.2.14 m
c. .37 m
d. -.37 m
e.-.31
A block of mass m is initially at rest a height h above the bottom of a wedge of mass M = 4m, as shown in the diagram labeled “before”. The system is released from rest, and the second diagram shows the situation after the block has slid down the wedge and onto to the horizontal table below, with the block moving to the left with speed Vmm and the wedge moving to the right with speed VMM. All surfaces are frictionless and there are no external horizontal forces acting on the system.
Suppose the speed of the block after is slides onto the table is Vmm = 2.3 m/s. What was the starting height of the block h?
a. h = 0.34 m
b. h = 0.27 m
c. h = 0.54 m
d. h = 1.35 m
e. There is not enough information provided to determine h
Explanation / Answer
distance of centre of mass of system from mid point
=(m1x1 + m2x2 + m3x3) / (m1+m2+m3)
= [(62.8 x -4.9/2) + (83.7 x 4.9/2) + (20.6 x 0) ] / (62.8 + 83.7 + 20.6)
= 0.306 m to right from centre.
finally all the component of system comes to centre.
so centre of plank will move to centre of mass position of system
displacement = 0.306 m = 0.31 m
Ans(a)
using momentum conservation,
initial momentum of system = final momentum of system
0 = (m x -2.3) + (4m x v)
v = 0.575 m/s
now using energy conservation,
mgh = (m 2.3^2 /2 ) + (4m x 0.575^2 /2 )
9.8 x h = 2.645 + 0.661
h = 0.34 m