a 3.0 kg block slides along a frictionless horizontal surface with a soeed of 7

Question

a 3.0 kg block slides along a frictionless horizontal surface with a soeed of 7 m/s. after sliding a distance of 2 m the block makes a smooth transition to a frictionless ramp inclined at an angle of 40 to the horizontal :

a- what distance along the ramp does the block slide before coming momentarily to rest ?

b-describe the motion block(if any) after it momentarliy comes to rest ?

2- a 5 kg block moving at 4.0 m/s collides and sticks with a second stationary block of mass 3.0 kg

a- find the velocity of blocks after the collision

b-what percentage of the initial kinetic energy of the blocks is lost during this collision ?

Explanation / Answer

mass 3 kg
speed v=7m/s
from conservation of energy
0.5mv^2=mgh
h=v^2/2g =7^2/19.6 =2.5 m
from
distance d =h/sin40 =2.5/sin40 =3.889 m
2.
a.
from conservation of momentum
5(4)+3(0) =(5+3)v
v=20/8 = 2.5 m/s
b)
initial kinetic energy =0.5*5*4^2+0 =40 J
final kinetic energy =0.5(3+5)*2.5^2 =25 J
percentage of the initial kinetic energy of the blocks is lost during this collision = 25/40)*100 =62.5%

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