A horizontal slingshot consists of two light, identical springs (with spring constants of 37.7 N/m) and a light cup that holds a 1.37-kg stone. Each spring has an equilibrium length of 50 cm. When the springs are in equilibrium, they line up vertically. Suppose that the cup containing the mass is pulled to x = 0.7 m to the left of the vertical and then released.
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(a) Stretch in the spring is
L₁=sqrt(x²+L₀²) = sqrt(0.7² +0.5²)=0.86 m
Elongation is
Δx= L₁-L₀= 0.86-0.5=0.36 m.
E(total) = PE=2•k•Δx²/2=2•37.7•0.36²/2=4.9 J.
(b) PE=KE =mv²/2
v=sqrt(2•PE/m) = sqrt(2•4.9/1.37) = 2.67 m/s
L₁=sqrt(x²+L₀²) = sqrt(0.7² +0.5²)=0.86 m
Elongation is
Δx= L₁-L₀= 0.86-0.5=0.36 m.
E(total) = PE=2•k•Δx²/2=2•37.7•0.36²/2=4.9 J.
(b) PE=KE =mv²/2
v=sqrt(2•PE/m) = sqrt(2•4.9/1.37) = 2.67 m/s
A horizontal slingshot consists of two light, identical springs (with spring constants of 45.7 N/m) and a light cup that holds a 1.37-kg stone. Each spring has an equilibrium length of 50 cm. When the springs are in equilibrium, they line up vertically. Suppose that the cup containing the mass is pulled to x = 0.7 m to the left of the vertical and then released. Determine
a) the system’s total mechanical energy.
Tries 0/4
b) the speed of the stone at x = 0.
a) the system’s total mechanical energy.
Tries 0/4
b) the speed of the stone at x = 0.
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