A bullet of mass m = 0.0010 kg embeds itself in a wooden block with mass M = 0.999 kg, which then compresses a spring (k = 140 N/m) by a distance 𝓍 = 0.050 m before coming to rest. The coefficient of kinetic friction between the block and table is μ = 0.50. What fraction of the bullet’s initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?

In Problems $76, 77, 78,$ and $79$ you are given the equation(s) used to solve a problem. For each of these, you are to finish the solution of the problem, including a pictorial representation.

$\frac{1}{2} (0.30 \text{ kg}) (0 \text{ m/s})^2 + \frac{1}{2} (3.0 \text{ N/m}) (\Delta x_2)^2 = \frac{1}{2} (0.30 \text{ kg}) (v_{1x})^2 + \frac{1}{2} (3.0 \text{ N/m}) (0 \text{ m})^2$

An 8g piece of sticky clay strikes and embeds itself in a 0.992kg block at rest on a frictionless, horizontal surface. The block is attached to a spring with a spring constant of 5N/m. The impact compresses the spring 75.0 cm. What was the initial speed of the clay?

One end of a massless, 30-cm-long spring with spring constant 15 N/m is attached to a 250 g stationary air-track glider; the other end is attached to the track. A 500 g glider hits and sticks to the 250 g glider, compressing the spring to a minimum length of 22 cm. What was the speed of the 500 g glider just before impact?

A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.13 shows the glider's velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring?

A bullet of mass m = 0.0010 kg embeds itself in a wooden block with mass M = 0.999 kg, which then compresses a spring (k = 140 N/m) by a distance 𝓍 = 0.050 m before coming to rest. The coefficient of kinetic friction between the block and table is μ = 0.50. What is the initial velocity (assumed horizontal) of the bullet?

In Problems $76,77,78,$ and $79$ you are given the equation(s) used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation(s).

$\frac{1}{2}\left(0.30\text{ kg}\right)(0\text{ m/s}{)}^2+\frac{1}{2}(3.0\text{ N/m}\left)\right(\Delta x_2{)}^2=\frac{1}{2}\left(0.30\text{ kg}\right)(v_{1x}{)}^2+\frac{1}{2}(3.0\text{ N/m}\left)\right(0\text{ m}{)}^2$

In Problems $76, 77, 78,$ and $79$ you are given the equation(s) used to solve a problem. For each of these, you are to finish the solution of the problem, including a pictorial representation.

$\frac{1}{2} (0.30 \text{ kg}) (0 \text{ m/s})^2 + \frac{1}{2} (3.0 \text{ N/m}) (\Delta x_2)^2 = \frac{1}{2} (0.30 \text{ kg}) (v_{1x})^2 + \frac{1}{2} (3.0 \text{ N/m}) (0 \text{ m})^2$