A machine pulls a 46 kg trunk 3.0 m up a 42o ramp at constant velocity, with the machine's force on the trunk directed parallel
2 answers:
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
= μθ ×d
= 0.36 ×46×9.8×cos42×3
= 361.81 J
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Answer:
q = 8.61 10⁻¹¹ m
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Explanation:
In this exercise we have two forces in balance: the electric force and the gravitational force
F_e -F_g = 0
F_e = F_g
Since the gravitational force is always attractive, the electric force must be repulsive, which implies that the electric charge in the two ships must be of the same sign.
Let's write Coulomb's law and gravitational attraction
In the exercise, indicate that the two ships are identical, therefore the masses of the ships are the same and we will place the same charge on each one.
k q² = G m²
q = m
we substitute
q = m
q = m
q = 0.861 10⁻¹⁰ m
q = 8.61 10⁻¹¹ m
This amount of charge does not depend on the distance between the two ships.
It is also proportional to the mass of the ships with the proportionality factor found.
Suppose the ships have a mass of m = 1000 kg, let's find the cargo
q = 8.61 10⁻¹¹ 10³
q = 8.61 10⁻⁸ C
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