Two whistles blow at the same time. The first whistle has a frequency twice that of the second whistle (it is a higher pitch). W
1 answer:
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Answer:
The horizontal component of her velocity is approximately 1.389 m/s
The vertical component of her velocity is approximately 7.878 m/s
Explanation:
The given question parameters are;
The initial velocity with which Margaret leaps, v = 8.0 m/s
The angle to the horizontal with which she jumps, θ = 80° to the horizontal
The horizontal component of her velocity, vₓ = v × cos(θ)
∴ vₓ = 8.0 × cos(80°) ≈ 1.389
The horizontal component of her velocity, vₓ ≈ 1.389 m/s
The vertical component of her velocity, = v × sin(θ)
∴ = 8.0 × sin(80°) ≈ 7.878
The vertical component of her velocity, ≈ 7.878 m/s.
Answer:
a) k = 200 N/m
b) E = 4 J
c) Δx = 6.3 cm
Explanation:
a)
- In order to find force constant of the spring, k, we can use the the Hooke's Law, which reads as follows:
- where F = 40 N and Δx =- 0.2 m (since the force opposes to the displacement from the equilibrium position, we say that it's a restoring force).
- Solving for k:
b)
- Assuming no friction present, total mechanical energy mus keep constant.
- When the spring is stretched, all the energy is elastic potential, and can be expressed as follows:
- Replacing k and Δx by their values, we get:
c)
- When the object is oscillating, at any time, its energy will be part elastic potential, and part kinetic energy.
- We know that due to the conservation of energy, this sum will be equal to the total energy that we found in b).
- So, we can write the following expression:
- Replacing the right side of (5) with (4), k, m, and v by the givens, and simplifying, we can solve for Δx₁, as follows:
⇒
⇒