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dimaraw [331]
3 years ago
9

Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle θ. A car can safely tr

avel along the unbanked curve at a maximum speed v0 under conditions when the coefficient of static friction between the tires and the road is 0.563. The banked curve is frictionless, and the car can negotiate it at the same speed v0. Find the angle θ of the banked curve.
Physics
1 answer:
Leviafan [203]3 years ago
7 0

Answer:

θ = 29.38°

Explanation:

The centripetal force is given by the formula;

F_c = F_n(sin θ) = mv²/r

Now, the vertical component of the normal force is; F_n(cos θ)

Now, this vertical component is also expressed as; F_n(cos θ) = mg

Thus, the slope is;

F_n(sin θ)/F_n(cos θ) = (mv²/r)/mg

tan θ = v²/rg

v² = rg(tan θ)

The initial speed will be gotten from the relation;

(v_o)² = μ_s(gr)

Plugging rg(tan θ) for (v_o)², we have;

μ_s(gr) = rg(tan θ)

rg will cancel out to give;

μ_s = (tan θ)

Thus, θ = tan^(-1) μ_s

μ_s is coefficient of static friction given as 0.563

θ = tan^(-1) 0.563

θ = 29.38°

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A car travels a distance of 100 km. For the first 30 minutes it is driven at a constant speed of 80 km/hr. The motor begins to v
gregori [183]

Explanation:

First, we need to determine the distance traveled by the car in the first 30 minutes, d_{\frac{1}{2}}.

Notice that the unit measurement for speed, in this case, is km/hr. Thus, a unit conversion of from minutes into hours is required before proceeding with the calculation, as shown below

                                          d_{\frac{1}{2}\text{h}} \ = \ \text{speed} \ \times \ \text{time taken} \\ \\ \\ d_{\frac{1}{2}\text{h}} \ = \ 80 \ \text{km h}^{-1} \ \times \ \left(\displaystyle\frac{30}{60} \ \text{h}\right) \\ \\ \\ d_{\frac{1}{2}\text{h}} \ = \ 80 \ \text{km h}^{-1} \ \times \ 0.5 \ \text{h} \\ \\ \\ d_{\frac{1}{2}\text{h}} \ = \ 40 \ \text{km}

Now, it is known that the car traveled 40 km for the first 30 minutes. Hence, the remaining distance, d_{\text{remain}} , in which the driver reduces the speed to 40km/hr is

                                             d_{\text{remain}} \ = \ 100 \ \text{km} \ - \ 40 \ \text{km} \\ \\ \\ d_{\text{remain}} \ = \ 60 \ \text{km}.

Subsequently, we would also like to know the time taken for the car to reach its destination, denoted by  t_{\text{remian}}.

                                              t_{\text{remain}} \ = \ \displaystyle\frac{\text{distance}}{\text{speed}} \\ \\ \\ t_{\text{remain}} \ = \ \displaystyle\frac{60 \ \text{km}}{40 \ \text{km hr}^{-1}} \\ \\ \\ t_{\text{remain}} \ = \ 1.5 \ \text{hours}.

Finally, with all the required values at hand, the average speed of the car for the entire trip is calculated as the ratio of the change in distance over the change in time.

                                                     \text{speed} \ = \ \displaystyle\frac{\Delta d}{\Delta t} \\ \\ \\ \text{speed} \ = \ \displaystyle\frac{100 \ \text{km}}{(0.5 \ \text{hr} \ + \ 1.5 \ \text{hr})} \\ \\ \\ \text{speed} \ = \ \displaystyle\frac{100 \ \text{km}}{2 \ \text{hr}} \\ \\ \\ \text{speed} \ = \ 50 \ \text{km hr}^{-1}

Therefore, the average speed of the car is 50 km/hr.

8 0
2 years ago
Write down one fact about each of the following crust, mantle, outer, core, & inner core
Oksanka [162]

Answer:

Hope this help you!!

Explanation:

Crust : The crust is the thinnest layer of the Earth. It has an average thickness of about 18 miles below land, and around 6 miles below the oceans. The crust is the layer that makes up the Earth's surface and it lies on top of a harder layer, called the mantle.

Mantle : The mantle is the mostly-solid bulk of Earth's interior. The mantle lies between Earth's dense, super-heated core and its thin outer layer, the crust. The mantle is about 1,802 miles thick, and makes up a whopping 84% of Earth's total volume

Outer Core : The outer core is the third layer of the Earth. It is the only liquid layer, and is mainly made up of the metals iron and nickel, as well as small amounts of other substances. The outer core is responsible for Earth's magnetic field. As Earth spins on its axis, the iron inside the liquid outer core moves around.

Inner Core : It's Almost The Size of the Moon. The Earth's inner core is surprisingly large, measuring 1,516 miles across. It's Mostly Made of Iron. It Spins Faster Than the Surface of the Earth. It Creates a Magnetic Field.

5 0
3 years ago
It is 5.00 km from your home to the physics lab. As part of your physical fitness program, you could run that distance at 10.0 k
8_murik_8 [283]

Answer:

a. Walking burns up more energy.

b. 1740 kJ

c. This is because more intense exercise releases a lot of energy in a short period of time, whereas, less intense energy releases it energy gradually over a long period of time.

Explanation:

a. We know energy W = Pt where P = power and t = time.

Now for walking, t = d/v where d = distance = 5.00 km and v = speed = 3.00 km/hr and P = 290 W

So, t = d/v = 5.00 km/3.00 km/hr = 5/3 hr = 5/3 × 3600 s = 6000 s

W = Pt = 290 W × 6000 s = 1740000 = 1740 kJ

Now for running, t = d/v where d = distance = 5.00 km and v = speed = 10.00 km/hr

So, t = d/v = 5.00 km/10.00 km/hr = 0.5 hr = 0.5 × 3600 s = 1800 s and P = 700 W

W = Pt = 700 W × 1800 s = 1260000 = 1260 kJ

Since walking burns up 1740 kJ and running burns up 1260 kJ, walking burns up more energy.

b. It burns up 1740 kJ

c. This is because more intense exercise releases a lot of energy in a short period of time, whereas, less intense energy releases it energy gradually over a long period of time.

4 0
3 years ago
While operating a vehicle on any highway of this state, it is illegal to physically hold or support a wireless device with any p
algol13

Answer:

True

Explanation:

In Massachusetts it's illegal to drive while texting or on your phone.

3 0
3 years ago
Which statement best describes the situation? Which statement best describes the situation? The car has the greater change of mo
Pachacha [2.7K]

Complete Question

A truck going 15 km/h has a head-on collision with a small car going 30 km/h. Which statement best describes the situation?

A. the truck has the greater change of momentum because it has the greater mass

B. the car has the greater change of momentum because it has the greater speed

C. neither the car nor the truck changes its momentum in the collision because momentum is conserved

D. they both have the same change in magnitude of momentum because momentum is conserved

E. none of the above is necessarily true

Answer:

D. They both have the same change in magnitude of momentum because     momentum is conserved

Explanation:

In order to get a good understanding of the solution above we define some

concetps

   Momentum

This is defines quantified motion and can be mathematically represented as  

      Momentum =  Mass of the body × Velocity of the body

According to the Law of conservation of momentum states that when two particles collide together in a system that is being isolated that their total momentum before and after their collision is equal this means that the momentum lost by the truck would be the same as the momentum gained by the small car

4 0
3 years ago
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