The force applied to lift the crate is 171 N
Explanation:
The lever works on the principle of equilibrium of moments, so we can write:

where
is the force in input
is the arm of the input force
is the output force
is the arm of the output force
For the lever in this problem, we have:


(force applied)
Solving the equation for
, we find the force applied to lift the crate:

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Answer:
v = 8.09 m/s
Explanation:
For this exercise we use that the work done by the friction force plus the potential energy equals the change in the body's energy.
Let's calculate the energy
starting point. Higher
Em₀ = U = m gh
final point. To go down the slope
Em_f = K = ½ m v²
The work of the friction force is
W = fr L cos 180
to find the friction force let's use Newton's second law
Axis y
N - W_y = 0
N = W_y
X axis
Wₓ - fr = ma
let's use trigonometry
sin θ = y / L
sin θ = 11/110 = 0.1
θ = sin⁻¹ 0.1
θ = 5.74º
sin 5.74 = Wₓ / W
cos 5.74 = W_y / W
Wₓ = W sin 5.74
W_y = W cos 5.74
the formula for the friction force is
fr = μ N
fr = μ W cos θ
Work is friction force is
W_fr = - μ W L cos θ
Let's use the relationship of work with energy
W + ΔU = ΔK
-μ mg L cos 5.74 + (mgh - 0) = 0 - ½ m v²
v² = - 2 μ g L cos 5.74 +2 (gh)
v² = 2gh - 2 μ gL cos 5.74
let's calculate
v² = 2 9.8 11 - 2 0.07 9.8 110 cos 5.74
v² = 215.6 -150.16
v = √65.44
v = 8.09 m/s
Answer:
D) 11 m/s
Explanation:
The problem asks us to calculate the velocity of the hot dog with respect to the observer stationary outside the train. This velocity is given by:

where
is the velocity of the train (towards right)
is the velocity of the man (towards right)
is the velocity of the hot-dog (towards left, so we put a negative sign)
Substituting the numbers into the equation, we find

and the positive sign means the velocity is toward right.
Answer:
Energy = 1.38*10^13 J/mol
Explanation:
Total number of proton in F-19 = 9
Total number of neutron in F-19 = 10
Expected Mass of F-19
= 9*1.007 + 10*1.008 = 19.152 u
Actual mass of F-19 = 18.998 u
Energy of one particle of F-19 = 931.5*Δm = 931.5*(19.152-18.998)
= 143.234 MeV
Energy of one mole of F-19 = 143.234*10^6*1.6*10^-19*6.022*10^23
= 1.38*10^13 J/mol