a)Cơ năng vật: \(W=\dfrac{1}{2}k\left(\Delta l\right)^2=\dfrac{1}{2}\cdot50\cdot0,05^2=0,0625J\)
b)Vận tốc khi lò xo bị biến dạng:
\(\dfrac{1}{2}mv^2=W\Rightarrow v=\sqrt{\dfrac{2W}{m}}=\sqrt{\dfrac{2\cdot0,0625}{0,8}}=0,4\)m/s
c)Khi \(W_đ=W_t\Rightarrow W'=2W_t=2mgz\)
Bảo toàn cơ năng: \(W=W'\)
\(\Rightarrow0,0625=2mgz\Rightarrow z=\dfrac{0,0625}{2\cdot0,8\cdot10}\approx4\cdot10^{-3}m=4mm\)
a) Cơ năng:
\(W_t=\dfrac{1}{2}mv^2+\dfrac{1}{2}k\left(\Delta l\right)^2=\dfrac{1}{2}\times0.8\times0^2+\dfrac{1}{2}\times50\times0.05^2=0.0625\left(J\right)\)
Do bỏ qua sức cản môi trường nên cơ năng bảo toàn
\(W_1=W=0.0625\left(J\right)\)
b) Vận tốc khi lò xo ko bị biến dạng:
\(0.0625=\dfrac{1}{2}\times0.8\times v^2+\dfrac{1}{2}\times50\times0^2\)
\(\Leftrightarrow v\approx0.4\)\((m/s)\)
c) \(W_đ=W_t\Leftrightarrow\left\{{}\begin{matrix}W_đ-W_t=0\\W_đ+W_t=0.0625\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}W_đ=0.03125\\W_t=0.03125\end{matrix}\right.\)
Khi \(W_đ=W_t\)
\(\Leftrightarrow W_t=\dfrac{1}{2}\times50\times\left(\Delta l\right)^2\)
\(\Leftrightarrow0.03125=\dfrac{1}{2}\times50\times\left(\Delta l\right)^2\)
\(\Leftrightarrow\Delta l\approx0.035\left(m\right)\)
