Answer to Question #89962 in Classical Mechanics for Thanh

Question

This block is pushed by a spring attached to the wall, slides across the table, and then falls to the ground. The block has a mass m 1.35 kg. The spring constant is k = 560 N/m, and the spring has been compressed by 0.11 m. The block slides a distance d 0.65 m across the table of height h 0.75 m, find the speed of the block when it lands on the floor

Answer 1

The coefficient of kinetic friction:

$$\mu=0.16$$

From the conservation of energy:

$$0.5kx^2+mgh=0.5mv^2+\mu mgd$$

$$v=\sqrt{\frac{kx^2}{m}+2g(h-\mu d)}$$

$$v=\sqrt{\frac{(560)(0.11)^2}{1.35}+2(9.8)(0.75-0.16(0.65))}=4.2\frac{m}{s}$$