Question

2) At right is a U vs x graph.(assume all #'s are 3 sig figs) U (J) a) A 0.500 kg ball with a total energy of 4.00 J is located at x=6.00 m and is moving to the right 1) What is its approximate range of motion? (max and min values of x) ii) What is its acceleration when it is at x = 7.00m. iii) What is its maximum speed? b) A 0.100 bug with total energy 6.00 J starts at x=0.500 m and is moving to the right. i) Where does the bug stop? ii) Before the bug stops, at what locations does it feel the maximum magnitude force? iii) What is the magnitude of this maximum force? 0 1 2 3 4 5 6 x (m) 7 8 9 10

Answer 1

a)Range of motion is x=0 to x=10m

b)from the graph at x=7m, U=1.5J

According to work energy theorem U=W=F*x so $\frac{U}{x}=F\Rightarrow F=\frac{1.5}{7}=0.214N$

$F=ma\Rightarrow a=\frac{F}{m}=\frac{0.214}{0.5}=0.428m/s^{2}$

c) From the graph maximum energy=7J

$E=\frac{1}{2}mv^{2}\Rightarrow v=\sqrt{\frac{2E}{m}}=\sqrt{\frac{2\times 7}{0.5}}=5.29m/s$