Wednesday

April 1, 2015

April 1, 2015

Posted by **Chad** on Thursday, August 9, 2012 at 10:48am.

ramp, height h, is released. It slides down the ramp, angle θ, with friction, coefficient μ. Half way down the

ramp, it bumps into and sticks to another box, mass m 2 , and together, they slide to the bottom. If m 1 = 2.0 kg,m2= 3.0 kg, k = 500 N/m, Δx = 0.40 m, h = 5.0 m, μ= 0.30, θ= 30.0O, how long does it take both boxes to reach the bottom (starting from when the first box is released)? The spring is parallel to the ramp surface and the Δx is measured parallel to the ramp surface.

- Physics -
**Elena**, Thursday, August 9, 2012 at 3:53pmk •Δx²/2=m1•vₒ²/2, ….. (1)

vₒ = Δx•sqrt(k/m1) =0.4•sqrt(500/2) =6.32 m/s

The distance from start to the bottom is

s=h/sinθ = 5/0.5 = 10 m.

Two parts s1 = s2 =10/2 =5 m.

The law of conservation of energy for s1:

m1•vₒ²/2 +ΔPE-W(fr) = m1•v1²/2,

Taking into account (1) we obtain

k •Δx²/2 +m1•g•h/2 - μ•m1•g•cosθ•h/2•sinθ = m1•v1²/2

v1= sqrt{ k •Δx²/m1 +g•h[1- (μ/tanθ)] }=

=sqrt{500•0.16/2 +9.8•5•[1-(0.3/tan30º]} = 7.97 m/s.

From kinematics:

a1=(v1²-vₒ²)/2s = (7.97² - 6.32²)/2•5 = 2.358 m/s²

v1=vₒ +a•t1,

t1= (v1-vₒ)/a=(7.97-6.32)/2.358 =0.6997 = 0.7 s.

The law of conservation of linear momentum

m1•v1+0 =(m1+m2) •u,

u =m1•v1/(m1+m2) = 2•7.97/5=3.2 m/s.

The law of conservation of energy for s2:

(m1+m2)•u²/2 +ΔPE-W(fr) = m1•u1²/2,

(m1+m2)•u²/2 + (m1+m2)•g•h/2 - μ•(m1+m2)•g•cosθ•h/2•sinθ = (m1+m2)•u1²/2,

u1=sqrt{u²+g•h[1-(μ/tanθ)]} =

=sqrt{3.2² +9.8•5(1-0.3/tan30º)} =5.81 m/s,

From kinematics:

a=(u1²-u²)/2•s=(5.81²-3.2²)/2•5 = 2.352 m/s²

u1=u+a•t2

t2=(u1-u)/a=(5.81-3.2)/2.352 =1.1 s.

t= t1+t2 =0.7+1.1 =1.8 s.

**Answer this Question**

**Related Questions**

Physics - A box slides from rest down a frictionless ramp inclined at 35.0° with...

Physics - A block of mass m = 2.4 kg is released from rest at a height of H = 3....

physics - A dude is spinning a 1.0 kg mass on the end of a 1.5 meter string. He ...

Physics - A child's game consists of a block that attaches to a table with a ...

physics - A block of mass m = 2.7 kg is released from rest at a height of H = 0....

Physics - A block of mass m = 5.2 kg is released from rest at a height of H = 4....

Physics - A(n) 160 g block is pushed by an external force against a spring with ...

physics - The 2.kg mass is heading toward a ramp-there’s no friction. Notice ...

physics - A 10 kg block slides 4.0 m down a ramp (having a coefficient of ...

physics - A 5 kg block is placed near the top of a frictionless ramp, which ...