here,
the mass of crate , m = 9.2 kg
initial speed of crate , u = 1.54 m/s
force applied , F = 104 N
theta = 20.5 degree
coefficient of kinetic friction , uk = 0.4
s = 4.9 m
a)
the work done by the gravitational force on the crate , Fg = - m * g * s * sin(theta)
Fg = - 9.2 * 9.81 * 4.9 * sin(20.5) J = - 154.9 J
b)
the increase in internal energy , U = - uk * m * g * cos(theta) * s
U = - 0.4 * 9.2 * 9.81 * 4.9 * cos(20.5) J
U = 165.7 J
c)
the work done by applied force ,Wf = F * s * cos(0)
Wf = 104 * 4.9 J= 509.6 J
d)
using Work-energy theorm
Work done by all forces = change in kinetic energy
Wf - U + Wg = change in kinetic energy
change in kinetic energy = 509.6 - 165.7 - 154.9 J
change in kinetic energy = 189 J
e)
let the final velocity be v
change in kinetic energy = 0.5 * m * ( v^2 - u^2)
189 = 0.5 * 9.2 * ( v^2 - 1.54^2)
solving for v
v = 6.6 m/s
the final velocity is 6.6 m/s
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