Question

Problem 3 A 6-kg block is moving on a horizontal frictionless floor with a speed of 4 m/s when a constant horizontal force F is applied to the block. The speed of the block increases to 10 m/s within a distance of 5 m. Find (a) initial and final kinetic energy, and (b) the applied force F Problem 4 A0.50 kg block sliding on a horizontal frictionless surface with a speed of 2.5 m/s strikes a light spring that has a spring constant of 3000 N/m. (a) What is the total mechanical energy of the system (with respect to the horizontal surface)? (b) What is the maximum amount the spring will be compressed? Problem 5 A force of 20 N holds an ideal spring with a 30 N/m spring constant in compression. What is the potential energy stored in the spring?

Answer 1

3.

(a)

$K_i=\frac {1}{2}mv_i^2=\frac {1}{2}\cdot 6\cdot 4^2=48\: J$

$\\K_f=\frac {1}{2}mv_f^2=\frac {1}{2}\cdot 6\cdot 10^2=300\:J$

(b)

$F=\frac {m(v^2-u^2)}{2s}=\frac {6\cdot (10^2-4^2)}{2\cdot 5}\: N= 50.4\: N$

4.

(a)

$E=\frac {1}{2}mv^2=\frac {1}{2}\cdot 0.50\cdot 2.5^2= 1.56\: J$

(b)

$\frac {1}{2}kx^2=1.56$

$\frac {1}{2}\cdot 3000\cdot x^2=1.56$

$x=0.0322\: m$

5.

$F=kx$

$x=\frac {F}{k}=\frac {20}{30}\: m= 0.67\: m$

$U=\frac {1}{2}kx^2=\frac {1}{2}\cdot 30\cdot 0.67^2=6.73\: J$