Question

g The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distanced s traveled by the 30-kg cart before it comes to rest (a) if m approaches zero and (b) if m

Answer 1

Solution :

It is given that a system is released from rest where no slack is attached to the cable and the spring is unstretched.

Mass of the cart = 30 kg

Applying the conservation of energy of the system,

Loss of the gravitational potential energy (PE) = the energy stored in the spring.

i.e., $mg \Delta h = \frac{1}{2}kx^2$

      $mg (x\sin 25^\circ)=\frac{1}{2}kx^2$

      $(30 \times 9.81) (x\sin 25^\circ)=\frac{1}{2}(125)x^2$

       x = 1.98

Therefore the distance travelled by the 30 kg cart is 1.98 m.