Answer:
the answers are
W = 1271.256 J
= 361.81 J
Explanation:
The mass of the trunk (m) = 46kg
angle between the ramp and the horizontal (θ) = 42°
The trunk is pulled at a displacement (d) up the ramp = 3m
The coefficient of kinetic friction between the trunk and the ramp = 0.36
The trunk is moving with a constant velocity therefore the net force on it is zero, therefore the force required to move the trunk must be equal to the summation of forces opposing the trunk
The two forces opposing the trunk are
- the gravitational force directed down the ramp
and - the frictional force between the ramp and the trunk

We have to calculate the machine's force which is equal to sum of the

=
θ
μ× N
N = mgcosθ
μ
θ
F = mg (sinθ + μcosθ)
F = 46× 9.8 (sin42 + 0.36×cos42)
F= 450.8 (0.67 +0.27)
F = 450.8 × 0.94
F = 423.752N
to calculate the workdone on the trunk by the machine force
The workdone on the trunk is = W = F × dcosΘ
Θ = 0° because the trunk is directed parallel to the ramp
W =423.752× 3 cos 0
W = 423.752 ×3
W = 1271.256 J
(b) the increase in thermal energy of the trunk and the ramp
Friction converts mechanical energy into thermal energy, so multiplying the frictional force with the distance gives the thermal energy generated by the trunk
× d
= μ
θ ×d
= 0.36 ×46×9.8×cos42×3
= 361.81 J
Answer:
The angle of refraction for the ray moving through the liquid is = 32.3°
Explanation:
Refractive index of liquid (n₁/n₂) = sini/sinr
∴ n₁/n₂ = sini/sinr ................ equation 1
n₁ = index of refraction for glass, n₂ = index of refraction for liquid
Where i = incident angle of the first medium, r = angle of refraction or angle in the second medium.
Since the light ray is traveling from glass - to - liquid, the first medium is glass and the second medium is liquid. and the refractive index will be that liquid with respect to glass.
using the equation,
n₁/n₂ = sini/sinr
i = 35° , n₁ = 1.52, n₂= 1.63
Making sinr the subject of the equation above,
sinr = sini/(n₁/n₂)
sinr = sin35(1.52)/1.63
sinr =0.574(1.52)/1.63
sinr = 0.535
Taking the sin inverse of both side of the equation
sin⁻¹(sinr) = sin⁻¹(0.535)
∴ r = 32.3°
The angle of refraction for the ray moving through the liquid is = 32.3°
The right option is (b). 32.3°
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