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3 years ago

9

Suppose the posted designated speed for a highway ramp is to be 30 mph and the radius of the curve is 700 ft. At what angle must

the curve be banked? No Friction

1 answer:

Basile [38]3 years ago

4 0

Answer:

4.92°

Explanation:

The banking angle θ = tan⁻¹(v²/rg) where v = designated speed of ramp = 30 mph = 30 × 1609 m/3600 s = 13.41 m/s, r = radius of curve = 700 ft = 700 × 0.3048 m = 213.36 m and g = acceleration due to gravity = 9.8 m/s²

Substituting the variables into the equation, we have

θ = tan⁻¹(v²/rg)

= tan⁻¹((13.41 m/s)²/[213.36 m × 9.8 m/s²])

= tan⁻¹((179.8281 m²/s)²/[2090.928 m²/s²])

= tan⁻¹(0.086)

= 4.92°

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A 4.10 g bullet moving at 837 m/s strikes a 820 g wooden block at rest on a frictionless surface. The bullet emerges, traveling

atroni [7]

Answer:

(a) 1.85 m/s

(b) 4.1 m/s

Explanation:

Data

bullet mass, Mb = 4.10 g

initial bullet velocity, Vbi = 837 m/s

wooden block mass, Mw = 820 g

initial wooden block velocity, Vwi = 0 m/s

final bullet velocity, Vbf = 467 m/s

(a) From the conservation of momentum:

Mb*Vbi + Mw*Vwi = Mb*Vbf + Mw*Vwf

Mb*(Vbi - Vbf)/Mw = Vwf

4.1*(837 - 467)/820 = Vwf

Vwf = 1.85 m/s

(b) The speed of the center of mass speed is calculated as follows:

V = Mb/(Mb + Mw) * Vbi

V = 4.1/(4.1 + 820) * 837

V = 4.1 m/s

6 0

3 years ago

These are the types of attractions found between molecules. Their strength determines the state of the substance at room tempera

VLD [36.1K]

Answer:

Intermolecular forces

Explanation:

The force of attractions that act between molecules are called intermolecular forces.

Their nature is electromagnetic, this means that they are just an expression of the electromagnetic force.

One example of intermolecular force is the ionic bond: this type of bond occurs when there are two ions, one positively charged and the other one negatively charged, and they are attracted by each other due to the electrostatic force, which therefore creates a bond between them.

Other types of intermolecular forces include:

Hydrogen bond

Ion-dipole forces

Van der Waals forces

The strength of these intermolecular forces determine the state of the substance. In fact, in solids, these forces are very strong, so that the molecules are strongly bond to each other and they cannot move freely, but only vibrate about their fixed position. On the other hand, in gases, these forces are very weak, therefore the molecules are able to move freely away from each other.

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3 years ago

A dentist using a dental drill brings it from rest to maximum operating speed of 391,000 rpm in 2.8 s. Assume that the drill acc

krek1111 [17]

Answer:

a

$\alpha = 2327.7 \ rev/s^2$

b

$\theta = 9124.5 \ rev$

Explanation:

From the question we are told that

The maximum angular speed is $w_{max} = 391000 \ rpm = \frac{2 \pi * 391000}{60} = 40950.73 \ rad/s$

The time taken is $t = 2.8 \ s$

The minimum angular speed is $w_{min}= 0 \ rad/s$ this is because it started from rest

Apply the first equation of motion to solve for acceleration we have that

$w_{max} = w_{mini} + \alpha * t$

=> $\alpha = \frac{ w_{max}}{t}$

substituting values

$\alpha = \frac{40950.73}{2.8}$

$\alpha = 14625 .3 \ rad/s^2$

converting to $rev/s^2$

We have

$\alpha = 14625 .3 * 0.159155 \ rev/s^2$

$\alpha = 2327.7 \ rev/s^2$

According to the first equation of motion the angular displacement is mathematically represented as

$\theta = w_{min} * t + \frac{1}{2} * \alpha * t^2$

substituting values

$\theta = 0 * 2.8 + 0.5 * 14625.3 * 2.8^2$

$\theta = 57331.2 \ radian$

converting to revolutions

$revolution = 57331.2 * 0.159155$

$\theta = 9124.5 \ rev$

6 0

3 years ago

A star near the visible edge of a galaxy travels in a uniform circular orbit. It is 41,200 ly (light-years) from the galactic ce

Ronch [10]

The total mass of the galaxy is 443.4 Solar mass

Orbital velocity ( $v$ ) = $\sqrt{\frac{MG}{R} }$

where M= weight of galaxy

G= gravitational constatnt = $6.674*10^-^1^1$ (given)

R = distance from centre = $41200$ Light years (given)= $4.12*9.5*10^1^6$ km (1 ly= $9.5*10^3$ billion km)

v= orbital velocity = $275$ $km/s$ (given)

∴ According to the formula

$(2.75*10^2)^2$ = $\frac{M*6.674*10^-^1^1}{4.12*9.5*10^1^6}$

⇒ $7.56*10^4*4.12*9.5*10^1^6=M*6.674*10^-^1^1$ (cross multiplying and expanding)

⇒ $29.59*10^2^1=M*6.674*10^-^1^1$

⇒ $\frac{29.59*10^2^1*10^1^1}{6.674}=M$

⇒ $4.434*10^3^2=M$

1 solar mass = $1.989*10^3^0 kg$

⇒ Mass in solar mass =443.4 Solar mass

⇒ M = 443.4 Solar mass

Learn more about Orbital velocity here :

brainly.com/question/22247460

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6 0

2 years ago

A china dish falls from a height of 1.5 m above the floor. Calculate its velocity just before it

alexandr402 [8]

Answer:

12m/s

Explanation:

v^2=u^2+2as

v=?

u=0 (the dish was stationary before it fell)

a=9.81 m/s^2 (acceleration due to gravity/freefall)

s=1.5m (the drop height)

So: v^2=0+2.9.81.1.5 = 144.35415

and therefore v=sqrt 144.35415

12x12=144 so I'd say v=12m/s

6 0

3 years ago