A 20.0 kg block is connected to a 30.0 kg block by a string that passes over a light frictionless pulley. The 30.0 kg block is connected to a spring that has negligible mass and a force constant of 240 N/m, as shown in Figure P8.59. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0 kg block is pulled 22.0 cm down the incline (so that the 30.0 kg block is 42.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0 kg block is 20.0 cm above the floor (that is, when the spring is unstretched).

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20.0 kg
30.0 kg
20.0 cm
40.0°
A 20.0 kg block is connected to a 30.0 kg block by a string that passes over a light frictionless pulley. The
30.0 kg block is connected to a spring that has negligible mass and a force constant of 240 N/m, as
shown in Figure P8.59. The spring is unstretched when the system is as shown in the figure, and the
incline is frictionless. The 20.0 kg block is pulled 22.0 cm down the incline (so that the 30.0 kg block is
42.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0 kg block is
20.0 cm above the floor (that is, when the spring is unstretched).
Transcribed Image Text:20.0 kg 30.0 kg 20.0 cm 40.0° A 20.0 kg block is connected to a 30.0 kg block by a string that passes over a light frictionless pulley. The 30.0 kg block is connected to a spring that has negligible mass and a force constant of 240 N/m, as shown in Figure P8.59. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0 kg block is pulled 22.0 cm down the incline (so that the 30.0 kg block is 42.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0 kg block is 20.0 cm above the floor (that is, when the spring is unstretched).
Expert Solution
Step 1

Part(a)

Gravity is causing the blocks to move,

workgravity=Fnet.x=30 g-sin 40° 20 g0.2 m=33.6 J

Part(b)

The spring is also causing the blocks to move in some direction as the net force.

workspring=12kxi2-12kxf2=12(250 N/m)(0.2 m)2-12(250 N/m)(0)2=50 J

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