Question
A 6.00-kg block is moving at Vo=5.00m/s along africtionless, horizontal surface toward a spring with forceconstant k=450N/m that is attached to a wall. The spring hasnegligible mass. a)Find the maximum distance the spring will becompressed. b)If the spring is to compress by no more than 0.150m, whatshould be the maximum value of Vo? A 6.00-kg block is moving at Vo=5.00m/s along africtionless, horizontal surface toward a spring with forceconstant k=450N/m that is attached to a wall. The spring hasnegligible mass. a)Find the maximum distance the spring will becompressed. b)If the spring is to compress by no more than 0.150m, whatshould be the maximum value of Vo?
Explanation / Answer
Kinetic energy of the block = Potential energy of thespring ( 1 / 2 ) m v o2 = ( 1/ 2) k x2 m v o2 = k x 2 from this the maximum distance the spring will becompressed is x = v o [ m / k] ----- (1) where m = mass of the block = 6 kg k= force constant =450N/m substitue values weget x = 0.57735 m (b). Maximum compression x ' = 0.150 m from eq( 1) , maximum speed V o =x ' [ k / m ] = 0.150 [ 450 / 6 ] = 1.299 m / s from this the maximum distance the spring will becompressed is x = v o [ m / k] ----- (1) where m = mass of the block = 6 kg k= force constant =450N/m substitue values weget x = 0.57735 m (b). Maximum compression x ' = 0.150 m from eq( 1) , maximum speed V o =x ' [ k / m ] = 0.150 [ 450 / 6 ] = 1.299 m / s