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viva [34]
2 years ago
13

A person driving her car at 43 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow

light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection (Fig. 2-29). The intersection is 15 m wide. Her car's maximum deceleration is -5.4 m/s2, whereas it can accelerate from 43 km/h to 70 km/h in 8.1 s. Ignore the length of her car and her reaction time.Figure 2-29If she hits the brakes, how far will she travel before stopping?
If she hits the gas instead, how far will she travel before the light turns red?m Should she try to stop, or should she speed up to cross the intersection before the light turns red?
Physics
1 answer:
siniylev [52]2 years ago
5 0

Answer:

If she hits the brakes, she will travel 13m before stopping. If she hits the gas, she will travel 28 before the light turns red. She should try to stop

Explanation:

To know how far she will travel before stopping, we need to use a kinematic formula which initial final velocity (Vf), initial velocity (V0), acceleration (a) and distance traveled(x):

V_{f}^{2}=V_{0} ^{2} +2ax

The moment in which she stops is when the final velocity equals zero. In this case, initial velocity is 43km/h=12m/s, and its maximum deceleration is -5.4m/s^2. Plugging in these values and solving for x:

0^2=(12m/s)^2+2(-5.4m/s)x\\x=13m

She will travel 13m before stopping

If she hits the gas, we need another kinematic formula, which relates distance traveled, initial speed, time (t) and acceleration.

x=v_{0}t+0.5a*t^2

If we know her car can accelerate from 43km/h=12m/s to 70km/h=19m/s in 8.1 s, we can know its acceleration:

a=\frac{19m/s-12m/s}{8.1s}=0.86m/s^2

In this case, the time before the light turns red is 2.0s. Plugging in all those values:

x=12m/s*2s+0.5*0.86m/s^2*(2s)^2=28m

If she hits the gas, she will travel 28m before the light turns red. She won't even reach the intersection, so she would try to stop.

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a)      K = 2/3 π G m ρ R₁³ / R₂ ,  b) U = - G m M / r

Explanation:

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     F = G m M / r²

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Let's use Newton's second law

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      G m M / R₂² = m v² / R₂

      v² = G M / R₂

They give us the density of the planet

    ρ = M / V

    V = 4/3 π R₁³

    M =   ρ V

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    v² = 4/3 π G  ρ R₁³ / R₂

    K = ½ m v²

    K = ½ m (4/3 π G ρ R₁³ / R₂)

    K = 2/3 π G m ρ R₁³ / R₂

Part B

Potential energy and strength are related

     F = - dU / dr

     ∫ dU = - ∫ F. dr

The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1

    U- U₀ = G m M ∫ dr / r²

    U - U₀ = G m M (- r⁻¹)

We evaluate for

    U - U₀ = -G m M (1 / r_{f} -  1 /r_{i})

They indicate that for ri = ∞     U₀ = 0

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3 years ago
A 60 kg sprinter has a momentum of +600 kg-m/s when he crosses the finish
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Answer:

10 ms⁻¹

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The amount of momentum that an object has is dependent upon two factors

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In terms of an equation,

Momentum (P) = Mass(m)×velocity(v)

                     P = m×v

                 600 = 60 × v ⇒ v = 10 ms⁻¹

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How much total work is done by the force in lifting the elevator from 0.0 m to 9.0 m?
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The total work is

         (mass of the elevator, kg) x (9.8 m/s²) x (9.0 m)           Joules .
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Below is a circuit schematic of sources and resistors (Figure 3). VS = 10V , R1 = 100Ω, R2 = 50Ω, R3 = 25Ω, IS = 2A. Calculate t
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So approximately 0.17  amps

and therefore, we can estimate the voltage drop (V3) in R3 uisng Ohm's law:

V_3=\frac{30}{175} *\,25=\frac{30}{7} \approx 4.28\,\,V

So now we know that the potential drop across the parellel resistors must be:

10 V -  4.28 V = 5.72 V

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