1- A car is traveling due west at 20.0 m/s. If the acceleration of the car is a

Question

1- A car is traveling due west at 20.0 m/s. If the acceleration of the car is a constant 1.0 m/s2 due west, find the velocity of the car after 3.00 s.

2- On a frictionless horizontal surface, a 1.50-kg mass traveling at 3.50 m/s suddenly collides with and sticks to a 3.00-kg mass that is initially at rest, as shown in the figure. This system then runs into an ideal spring of force constant (spring constant) 50.0 N/cm. What will be the maximum compression distance of the spring?

3- A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0kg box. The larger box is attached to an ideal spring of force constant (spring constant) 150 N/m, as shown in the figure. Find the amplitude of the resulting oscillations of this system. what is the period of the oscillations?

Explanation / Answer

1) v = u + a*t

= 20 + 1*3

= 23 m/s due west

2) First Apply momnetum conservation,

m1*u1 = (m1+m2)*v

v = m1*u1/(m1+m2)

= 1.5*3.5/(1.5+3)

= 1.17 m/s

K = 50 N/cm = 5000 N/m

now Apply, Energy conservation

0.5*(m1+m2)*v^2 = 0.5*k*x^2

==> x = v*sqrt((m1+m2)/k)

= 1.17*sqrt((1.5+3)/5000)

= 0.035 m or 3.5 cm

3)

First Apply momnetum conservation,

m1*u1 = (m1+m2)*v

v = m1*u1/(m1+m2)

= 2*5/(2+6)

= 1.25 m/s

K = 150 N/m

now Apply, Energy conservation

0.5*(m1+m2)*v^2 = 0.5*k*A^2

==> A = v*sqrt((m1+m2)/k)

= 1.25*sqrt((2+6)/150)

= 0.035 m or 3.5 cm

= 0.29 m or 29 cm

w = sqrt(k/(m1+m2))

= sqrt(150/(2+6))

= 4.33 rad/s

w = 2*pi/T

T = 2*pi/w

= 2*pi/4.33

= 1.45 s

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