Answer:
0.3 m
Explanation:
Initially, the package has both gravitational potential energy and kinetic energy. The spring has elastic energy. After the package is brought to rest, all the energy is stored in the spring.
Initial energy = final energy
mgh + ½ mv² + ½ kx₁² = ½ kx₂²
Given:
m = 50 kg
g = 9.8 m/s²
h = 8 sin 20º m
v = 2 m/s
k = 30000 N/m
x₁ = 0.05 m
(50)(9.8)(8 sin 20) + ½ (50)(2)² + ½ (30000)(0.05)² = ½ (30000)x₂²
x₂ ≈ 0.314 m
So the spring is compressed 0.314 m from it's natural length. However, we're asked to find the additional deformation from the original 50mm.
x₂ − x₁
0.314 m − 0.05 m
0.264 m
Rounding to 1 sig-fig, the spring is compressed an additional 0.3 meters.
Answer:
case x py L is in the positive z direction
case y px L the negative z direction
Explanation:
The angular amount is defined by the relation
L = r x p
the bold are vectors, where r is the position vector and p is the linear amount vector.
The module of this vector can be concentrated by the relation
L = r p sin θ
the direction of the vector L can be found by the right-hand rule where the thumb points in the direction of the displacement vector, the fingers extended in the direction of the moment p which is the same direction of speed and the palm points in the direction of the angular momentum L
in the case x py
the thumb is in the x direction, the fingers are extended in the direction and the palm is in the positive z direction
In the case y px
the thumb is in the y direction, the fingers are in the x direction, the palm is in the negative z direction
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