A block of mass m is dropped onto a relaxed vertical spring that has a spring co

Question

A block of mass m is dropped onto a relaxed vertical spring that has a spring constant kappa. The block becomes attached to the spring and compresses the spring a distance d before momentarily stopping. M = 250g k = 2.5 N/cm d = 12 cm While the spring is being compressed, write a model for the work that is done on the block by the gravitational force on it? For the same conditions as in part A, the model for work done by the spring force? Calculate the numerical values for part A and B using the given values. What is the model for the speed of the block just before it hits the spring? (Assume that friction is negligible. If the speed at impact is doubled, what is the maximum compression of the spring? Calculate the numerical values for parts D and F using the given values.

Explanation / Answer

here,

m = 0.25 kg

K = 2.5 N/cm

K = 250 N/m

d = 0.12 m

(a)

the work done on the block by gravitational force on it , wg = m*g*d

(b)

the work done by the spring force , Ws = - 0.5 * k*d^2

(c)

the work done on the block by gravitational force on it , wg = m*g*d

Wg = 0.25 * 9.8 * 0.12

Wg = 0.294 J

the work done on the block by gravitational force on it is 0.294 J

the work done by the spring force , Ws = - 0.5 * k*d^2

Ws = - 1.8 J

the work done by the spring force is - 1.8 J

(d)

let the speed of the block be v

0.5 * m*v^2 + m*g*d = 0.5*k*x^2

v = (sqrt( k*x^2 - 2*m*g*d))/m

the speed of the block just before it hits the spring is v = (sqrt( k*x^2 - 2*m*g*d))/m

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