A mass M = 1.0 kg rests on a horizontal rough surface is attached to two identic
ID: 2326943 • Letter: A
Question
A mass M = 1.0 kg rests on a horizontal rough surface is attached to two identical unstressed horizontal springs A and B, at right angles to each other as shown in the figure 3. The other end of each spring is attached to a friction less roller that always in contact with the track as shown in the figure 1 . The coefficient of friction between the mass and the horizontal surface is 0.5. Two perpendicular forces, FY and FX of variable magnitude simultaneously act on the mass M such that the mass moves very slowly along a straight line from its initial to final location which is 3.0 cm along the x-axis and 4.0 cm along the y-axis. Take acceleration due to gravity, g = 10 m/s^2.A. Find the maximum frictional force in Newtons. B. Find the maximum value of Fx in N C. Find the maximum value Fy in N D. Find work Wx in Joules done by force Fx E. Find work Wy in Joules done by force Fy
Track A Final E Location Spring A 3 cm. 100 N/m. 4 cm. 1 kg Force X Initial t Spring B location k 100 N/m. Force Y Track B
Explanation / Answer
a).
Write the equation for the friction force acting on the mass M
fs = mg
Where is coefficient of friction and m is the mass and g is the gravitational acceleration
Substitute = 0.5 , m = 1.0 kg and g = 10 m/s2
fs = (0.5)(1.0 kg)(10 m/s2 )
= 5 N Answer
b).
Write the equation for the maximum value of Fx
Fx = kA*x
Substitute kA = 100 N/m and x = 0.03 m
Fx =(100 N/m)*(0.03 m)
= 3 N Answer
c).
Write the equation for the maximum value of FY
FY = kBy + mg - fs
Substitute kB = 100 N/m, y = 0.04 m, m = 1.0 kg and g = 10 m/s2 and fs = 5 N
FY = (100 N/m)(0.04 m) + (1.0 kg)(10 m/s2) - 5 N
= 9 N Answer
d).
Write the equation for the work done by the Fx in Joules
Wx = Fx *x
Substitute Fx = 3 N and x = 0.03 m
Wx = (3 N)*(0.03 m)
= 0.09 Joules Answer
e).
Write the equation for the work done by the Fy in Joules
Wy = Fy *y
Substitute Fy = 9 N and y = 0.04 m
Wx = (9 N)*(0.04 m)
= 0.36 Joules Answer
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