A spring with a spring constant of 500 N/m is used to propel a 0.41-kg mass up a
ID: 1901368 • Letter: A
Question
A spring with a spring constant of 500 N/m is used to propel a 0.41-kg mass up an inclined plane. The spring is compressed 30 cm from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length l = 3 m and is inclined at 32?. Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of 0.35. When the spring is compressed, the mass is at distance d = 1.4 m from the bottom of the plane. (a) What is the speed of the mass as it reaches the bottom of the plane? (b) What is the speed of the mass as it reaches the top of the plane? (c) What is the total work done by friction from the beginning to the end of the mass's motion?
A spring with a spring constant of 500 N/m is used to propel a 0.41-kg mass up an inclined plane. The spring is compressed 30 cm from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length l = 3 m and is inclined at 32?. Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of 0.35. When the spring is compressed, the mass is at distance d = 1.4 m from the bottom of the plane. (a) What is the speed of the mass as it reaches the bottom of the plane? (b) What is the speed of the mass as it reaches the top of the plane? (c) What is the total work done by friction from the beginning to the end of the mass's motion?Explanation / Answer
a) energy theorem ,
spring to botttom of plane,
kx2 /2 = mg x d + mu2 /2
500 x 0.302 = 2 x 0.35 x 0.41 x 9.81 x 1.4 + 0.41 x u2
u = 10 m/s
b) bottom of plane to top of plane ,
m x 102 /2 = mglsin + mgcos x l + mv2 /2
50 = 9.81 x 3 x sin32 + 0.35 x 9.81 x cos32 x 3 + v2 /2
v = 7.165 m/s
c) work done by friction. = mg x d + mgcos x l = 0.35 x 0.41 x 9.81 x 1.4 + 0.35 x 0.41x 9.81 x cos32 x 3
W = 5.55 J
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