Mass m 1 = 4.0 kg lies on a table, pulled by another mass m 2 = 1.8 kg under the
ID: 1262845 • Letter: M
Question
Mass m1= 4.0 kg lies on a table, pulled by another mass m2= 1.8 kg under the effect of Earth's gravity. Assume the pulley to be frictionless and that the coefficient of friction between m1 and the table is 0.34. Initially, mass m2 is 0.81m above the floor, and mass m1 is 1.62 m to the left of the pulley.
a) What is in J the initial gravitational potential energy of the system made up of both masses (in your calculations, since m1 will not move off the table, assume its gravitational potential energy to be zero.)?
b) What is in J the initial mechanical energy of the system made up of both masses?
The system is let go, and shortly after, m2 hits the ground. For this problem, we will focus on the motion of the masses from the instant they were released to the instant m2 touches the ground.
c) What is in J the energy lost to friction as the masses move from the initial position until m2 touches the ground?
d) What is in J the mechanical energy of the system made up of both masses the instant m2 touches the ground?
e) With what velocity would m2 hit the ground? Provide the magnitude of the velocity in m/s.
Use 10.0 N/kg for g.
Mass m1= 4.0 kg lies on a table, pulled by another mass m2= 1.8 kg under the effect of Earth's gravity. Assume the pulley to be frictionless and that the coefficient of friction between m1 and the table is 0.34. Initially, mass m2 is 0.81m above the floor, and mass m1 is 1.62 m to the left of the pulley. a) What is in J the initial gravitational potential energy of the system made up of both masses (in your calculations, since m1 will not move off the table, assume its gravitational potential energy to be zero.)? b) What is in J the initial mechanical energy of the system made up of both masses? The system is let go, and shortly after, m2 hits the ground. For this problem, we will focus on the motion of the masses from the instant they were released to the instant m2 touches the ground. c) What is in J the energy lost to friction as the masses move from the initial position until m2 touches the ground? d) What is in J the mechanical energy of the system made up of both masses the instant m2 touches the ground? e) With what velocity would m2 hit the ground? Provide the magnitude of the velocity in m/s. Use 10.0 N/kg for g.Explanation / Answer
a) Potential energy of a mass = mgh
P.E. of system = 1.8 x 10 x 0.81 = 14.58 J
b) initialy it doesn't have any K.E.
total Mechanical energy = P.E. + K.E. = 14.58 + 0
= 14.58 J
c) m1 travels 0.81 m when m2 touches the ground.
friction force = u.m1g = 0.34 x 4 x 10 = 13.6 N
Energy lost = - work done = - ( -13.6 x 0.81) = 11.02 J
d) Total energy = initial M.E. - energy lost due friction
= 14.58 - 11.02 = 3.56 J
e) using
final energy = mv^2 /2
3.56 = (4 + 1.8)v^2 /2
v = 1.11 m/s