Dynamics ,dl 10% Mass and spring problem 9:57 PM MasteringEngineering MasteringC
ID: 1885370 • Letter: D
Question
Dynamics
,dl 10% Mass and spring problem 9:57 PM MasteringEngineering MasteringC...- The 4.5-kg mass moves along the surface shown. The roller attached to the spring keeps the mass in contact with the surface and also keeps the spring horizontal at all times while the mass moves down the surface 2-0.5 k10 N/m @ Tap image to zoom Part A If the spring has a stiffness of k 10 N/m, and unstretched length of 0.5 m, determine the normal force of the path on the block at the instant r 1 m when the block has a speed of 4 m/s. Neglect the mass of the roller and the spring Express your answer with the appropriate units. N-1 Value nitsExplanation / Answer
Given k=10
At x=1,y=1.5
The total extension is 1 m
Therefore the total force acting is 10N on the block
Assuming it as a weightless body on a frictionless surface,
The slope at that instant is dy/dx
dy/dx=-1 which is a slope of 45 degrees
Since the mass of block is 4.5 kg
The mass normal on the surface is mgcos
Which is 4.5*9.81*cos 45°=31.21N
The force due to the spring is also acting partially as normal core and partially to prevent the movement of the block downwards
The component acting as normal is 10*cos
=10*cos 45°
=7.07N .
Therefore the total normal force is 31.21+7.07 N
=38.28 N
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