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marishachu [46]
2 years ago
13

The x-coordinates of two objects moving along the x-axis are given as a function of time t. x1 = (4 m/s)t and x2 = −(159 m) + (2

4 m/s)t − (1 m/s2)t2 . Calculate the magnitude of the distance of closest approach of the two objects. x1 and x2 never have the same value.

Physics
1 answer:
SpyIntel [72]2 years ago
3 0
The x-coordinate of the first object is
x₁(t) = (4 m/s)t

The x-coordinate of the second object is
x₂(t) = -(159 m) + (24 m/s)t - (1 m/s²)t²

The distance between the two objects is
x(t) = x₂ - x₁ 
      =  - 159 + 24t - t² - 4t
      = -t² + 20t  - 159

Write this equation in the standard form for a parabola.
x = -[t² - 20t] - 159
   = -[(t - 10)² - 100] - 159
   = -(t-10)² - 59

This parabola has a vertex at (-10,  -59), and it is downward.
Because the maximum value of x is negative, the two objects never touch
The closest distance between the objects is 59 m.

The two graphs confirm that the analysis is correct.

Answer: The closest approach is 59 m.

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bazaltina [42]

Answer:

1. t_2 = 2t_1

2. t_2 = t_1\sqrt{2}

Explanation:

1. According to Newton's law of motion, the puck motion is affected by the acceleration, which is generated by the push force F.

In Newton's 2nd law: F = ma

where m is the mass of the object and a is the resulted acceleration. So in the 2nd experiment, if we double the mass, a would be reduced by half.

a_1 = 2a_2

Since the puck start from rest, in the 1st experiment, to achieve speed of v it would take t time

t = v / a_1

Now that acceleration is halved:

t = \frac{v}{2a_2}

\frac{v}{a_2} = 2t

You would need to push for twice amount of time t_2 = 2t_1

2. The distance traveled by the puck is as the following equation:

d = at^2

So if the acceleration is halved while maintaining the same d:

\frac{d_1}{d_2} = \frac{a_1t_1^2/2}{a_2t_2^2/2}

As d_1 = d_2, then d_1/d_2 = 1. Also a_1 = 2a_2

1 = \frac{2a_2t_1^2}{a_2t_2^2}

t_2^2 = 2t_1^2

t_2 = t_1\sqrt{2}\approx 1.14t_1

So t increased by 1.14

7 0
3 years ago
Please Help Meee
g100num [7]

Answer:

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4 0
2 years ago
If 1.00 mol of argon is placed in a 0.500-L container at 28.0 ∘C , what is the difference between the ideal pressure (as predict
Rudik [331]

Answer:

1.98 atm

Explanation:

Given that:

Temperature = 28.0 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (28 + 273.15) K = 301.15 K

n = 1

V = 0.500 L

Using ideal gas equation as:

PV=nRT

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 0.0821 L atm/ K mol  

Applying the equation as:

P × 0.500 L = 1 ×0.0821 L atm/ K mol  × 301.15 K

⇒P (ideal) = 49.45 atm

Using Van der Waal's equation

\left(P+\frac{an^2}{V^2}\right)\left(V-nb\right)=nRT

R = 0.0821 L atm/ K mol  

Where, a and b are constants.

For Ar, given that:

So, a = 1.345 atm L² / mol²

b =  0.03219 L / mol

So,  

\left(P+\frac{1.345\times \:1^2}{0.500^2}\right)\left(0.500-1\times 0.03219\right)=1\times 0.0821\times 301.15

P+\frac{1.345}{0.25}=\frac{24.724415}{0.46781}

P=\frac{24.724415}{0.46781}-\frac{1.345}{0.25}

⇒P  (real) = 47.47 atm

Difference in pressure = 49.45 atm - 47.47 atm = 1.98 atm

4 0
2 years ago
What happens to the current as we increase the amount of stepping of our transformer? Does this help explain why the primary was
matrenka [14]

Answer:

Current will decrease.

Explanation:

When we increase the number of stepping in transformer, the voltage will increase as its is directly proportional to the number of turn of stepping. Thus as the voltage will increase, current will decrease. As per the equation of ideal transformer,   E1 / E2 = I2 / I1

E1 and E2 are the voltages in primary and secondary winding and I1 and I2 are the current.

As the number of turns will be increased more inevitable losses will be generated that dissipates heat thus warming the primary.

Though the conservation of energy is obeyed but losses occur in this scenario hence step-up transformers cannot be used to create free energy.

7 0
2 years ago
You test a moon buggy on Earth. When the buggy hits a bump, it oscillates up and down on its springs with a period of 4 seconds.
Blizzard [7]

Answer:

Remains same

Explanation:

T = Time period of oscillation

m = mass

k = spring constant

Time period of oscillation is given as

T = 2\pi \sqrt{\frac{m}{k} }

we know that as we move from earth to moon, the value of spring constant "k"  and mass "m" remains unchanged because they do not depend on the acceleration due to gravity.

Time period depends on spring constant inversely and directly on the mass.

hence the time period remains the same.

3 0
3 years ago
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