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Simple Mass-Spring System Problem!
A mass M slides across a frictionless horizontal table with constant speed V_0_. It collides with a spring of spring constant k, compressing it. The mass-spring system then rebounds. Take the position of the mass when it first hits the spring to be x=0.
a) Suppose that the mass comes to a momentary stop after compressing the spring a distance L. What is the spring constant k in terms of V_0_, M, and L?
b) The spring reexpands, pushing the mass back. What is the speed of the mass M when it passes through x=0?
F_spring_ = k*d;
E_stored in spring_ = 1/2(k*d^2^)
a) E_i_ = E_f_
1/2mv^2^ = 1/2kx^2;
mv^2^ = kL^2
(mV_0_^2)/L^2 = k;
b) no idea
A mass M slides across a frictionless horizontal table with constant speed V_0_. It collides with a spring of spring constant k, compressing it. The mass-spring system then rebounds. Take the position of the mass when it first hits the spring to be x=0.
a) Suppose that the mass comes to a momentary stop after compressing the spring a distance L. What is the spring constant k in terms of V_0_, M, and L?
b) The spring reexpands, pushing the mass back. What is the speed of the mass M when it passes through x=0?
Homework Equations
F_spring_ = k*d;
E_stored in spring_ = 1/2(k*d^2^)
The Attempt at a Solution
a) E_i_ = E_f_
1/2mv^2^ = 1/2kx^2;
mv^2^ = kL^2
(mV_0_^2)/L^2 = k;
b) no idea