5 A cart with m 340kg rides on the track shown The track is

5. A cart with m= 3.40kg rides on the track shown. The track is frictionless except for a level section 0.40m long where .-0.54. The cart is initially at rest against spring I (k 1400N/m) which is compressed by 8.00cm. When released it travels along the track until it reaches spring 2 (k -800Nm) which it compresses until the cart stops. Ifh -0.38m and h2-0.14m, determine the speed of the cart at points A, B, C and D. Also how much will spring 2 be compressed at the end.

Solution

we will use conservation of energy

Elastic PE = KE

1/2 (1400) (0.08)^2 = 1/2 (3.40) v^2

v (elcoty at A) =1.623 m/s

for B

1/2 mv^2 + mgh = 1/2 m Vb^2

1/2 (2.634 ) + 9.8 (0.38) = 1/2 Vb^2

V ( velocity at B) = 3.175 m/s apprx

retardation for friction surface = a= 0.54 (9.8)=5.292 m/s^2

Vc^2 = Vb^2 - 2 (5.292) (0.4)

Vc^2= 9.5664

V ( velocity at C) = 3.1 m/s

1/2 m( 3.1)^2 = m(9.8) (0.14) + 1/2 m Vd^2

4.7832- 1.372 = 0.5 Vd^2

V ( velcity at D) = 2.61 m/s apprx

compression = x

1/2 ( 3.40)( 2.61)^2 = 1/2 ( 800) x^2

x= 0.17 m or 17 cm apprx