MAE 488 Test 2 UPDATED ACTUAL QUESTIONS AND
CORRECT Answers
states that the acceleration of a particles mass is Newtons 2nd Law
proportional to the net force acting upon it and is in the
direction of this force.
Newton's 2nd law states that the of a particle massacceleration; net force; force
is proportional to the acting upon it and is in the
direction of this _.
, Newton's 2nd Law representation -- ma = m (dv/dt) = f_net
-- ma = m(dv/dt) = m(d^2x/dt^2) = f_net
-- a(t) = dv/dt = v'(t) = d^2(x)/dt^2 = x''(t)
-- v(t) = dx/dt = x'(t)
Derive kinetic energy and work from newtons 2nd law --> m(dv/dt) = f(x)
(where force is a func. of displacement) multiply both sides by vdt
--> mvdv = vdtf(x)
--> (dx/dt)(dt)f(x) = f(x)dx
integrate
--> mv^2/2 = integral of f(x)dx + C
if the work done by the force is path independent, we conservative; f(x) = - dV/dx
say f(x) is a force and _ _.
in the equation for a conservative force, f(x) = -dV/dx, V Potential Energy function
is the _.
Derive potential energy and kinetic energy assuming --> f(x) = -dV/dx
conservative forces integrate
--> integral dV = - integral f(x)dx
--> V(x) = -[mv^2/2 - C]
--> V(x) + mv^2/2 = C
V(x) potential energy
mv^2/2 kinetic energy
If only conservative forces are considered, the of sum; constant
the kinetic and potential energy in a system is a _.
If only conservative forces are considered equations? change KE + change PE = 0
or
m/2(v^2 - v_0^2) + (V(x) - V(x_0)) = 0
For rotation about an axis, Newton's 2nd law becomes... I_0(α) = I_0(⍵') = I_0(θ'') = M_0
Mass moment of inertia is defined as.... I = ∫ r^2dm
The parallel axis theorem states that... I_a = I_s + md^2
The kinetic energy of a rotating body is... KE = 1/2(I)(ω)^2
Work done by rotating body is... W = ∫ from 0 to theta, Mdθ
Very often a system will have both and . translational ; rotational
If the motions are coupled, we can use the concept of translational, rotational
kinetic energy to convert a system to a purely _ or
purely model
Pure rolling motion occurs when so there is no f_t < μ_s N ; slipping; v = rω
between a wheel and a surface so that _.
Pure sliding motion occurs when a wheel is prevented rolling; ω = 0; v does not equal rω.
from so that and _.
CORRECT Answers
states that the acceleration of a particles mass is Newtons 2nd Law
proportional to the net force acting upon it and is in the
direction of this force.
Newton's 2nd law states that the of a particle massacceleration; net force; force
is proportional to the acting upon it and is in the
direction of this _.
, Newton's 2nd Law representation -- ma = m (dv/dt) = f_net
-- ma = m(dv/dt) = m(d^2x/dt^2) = f_net
-- a(t) = dv/dt = v'(t) = d^2(x)/dt^2 = x''(t)
-- v(t) = dx/dt = x'(t)
Derive kinetic energy and work from newtons 2nd law --> m(dv/dt) = f(x)
(where force is a func. of displacement) multiply both sides by vdt
--> mvdv = vdtf(x)
--> (dx/dt)(dt)f(x) = f(x)dx
integrate
--> mv^2/2 = integral of f(x)dx + C
if the work done by the force is path independent, we conservative; f(x) = - dV/dx
say f(x) is a force and _ _.
in the equation for a conservative force, f(x) = -dV/dx, V Potential Energy function
is the _.
Derive potential energy and kinetic energy assuming --> f(x) = -dV/dx
conservative forces integrate
--> integral dV = - integral f(x)dx
--> V(x) = -[mv^2/2 - C]
--> V(x) + mv^2/2 = C
V(x) potential energy
mv^2/2 kinetic energy
If only conservative forces are considered, the of sum; constant
the kinetic and potential energy in a system is a _.
If only conservative forces are considered equations? change KE + change PE = 0
or
m/2(v^2 - v_0^2) + (V(x) - V(x_0)) = 0
For rotation about an axis, Newton's 2nd law becomes... I_0(α) = I_0(⍵') = I_0(θ'') = M_0
Mass moment of inertia is defined as.... I = ∫ r^2dm
The parallel axis theorem states that... I_a = I_s + md^2
The kinetic energy of a rotating body is... KE = 1/2(I)(ω)^2
Work done by rotating body is... W = ∫ from 0 to theta, Mdθ
Very often a system will have both and . translational ; rotational
If the motions are coupled, we can use the concept of translational, rotational
kinetic energy to convert a system to a purely _ or
purely model
Pure rolling motion occurs when so there is no f_t < μ_s N ; slipping; v = rω
between a wheel and a surface so that _.
Pure sliding motion occurs when a wheel is prevented rolling; ω = 0; v does not equal rω.
from so that and _.
