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Dima020 [189]
3 years ago
15

A car is traveling in uniform circular motion on a section of flat roadway whose radius is . The road is slippery, and the car i

s just on the verge of sliding off the roadway. If the car’s speed were now doubled, what would be the smallest radius of the curve it could drive on without slipping?

Physics
1 answer:
Alona [7]3 years ago
8 0

Answer:

The smallest radius will be four (4) times the initial radius

Explanation:

The car maintains a constant angular speed. According to Newton's Second Law F = m a

1. F_{r}=m*A_{n}

2. A_{n}=\frac{v^2}{R_{p}}

Replacing 2 in 1

3. F_{r}=m*\frac{v^2}{R_{p}}

Where:

Fr= Frictional force

Rp= Initial Radius

An= Centripetal Acceleration

M= Mass

V= Velocity

Also we have that:

4. F_{r}=\mu *W=\mu*m*g

μ= Coefficient of friction between the car and the surface

M= Mass

W= Weight

G= Gravity

r is cleared from equation 3

5. R_{p}=m*\frac{v^2}{F_{r}}

Replacing 4 in 5

6. R_{p}=m*\frac{v^2}{\mu*m*g}

Simplifying

7. R_{p}=\frac{v^2}{\mu*g}

Now we have a new velocity equal to twice the initial velocity, We replace it by 2v in equation 7

8. R_{n}=\frac{(2v)^2}{\mu*g}

Computing

9. R_{n}=\frac{4v^2}{\mu*g}

Replacing 5 in 9

R_{n}=4*R_{p}

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A makes an angel of 30.0 above the positive x-axis, and B makes an angel of 45.0 below the negative x-axis. A=3.00 units and B=2
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20 cubic inches of a gas with an absolute pressure of 5 psi is compressed until its pressure reaches 10 psi. What's the new volu
Anna71 [15]

Answer:

B. V_{f}= 10\,cubic\,inches

Explanation:

Assuming we are dealing with a perfect gas, we should use the perfect gas equation:

PV=nRT

With T the temperature, V the volume, P the pressure, R the perfect gas constant and n the number of mol, we are going to use the subscripts i for the initial state when the gas has 20 cubic inches of volume and absolute pressure of 5 psi, and final state when the gas reaches 10 psi, so we have two equations:

P_{i}V_{i}=n_{i}RT_{i} (1)

P_{f}V_{f}=n_{f}RT_{f} (2)

Assuming the temperature and the number of moles remain constant (number of moles remain constant if we don't have a leak of gas) we should equate equations (1) and (2) because T_{i}=T_{f}, n_{i}=n_{f} and R is an universal constant:

P_{i}V_{i}= P_{f}V_{f}, solving for V_{f}

V_{f} =\frac{P_{i}V_{i}}{P_{f}} =\frac{(5)(20)}{10}

V_{f}= 10 cubic\,inches

6 0
3 years ago
Romeo (81.0 kg) entertains Juliet (53.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m awa
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Answer:

0.64 m

Explanation:

The first thing is calculate the center of mass of the system.

X_{cm}= \sum_{n=1}^{n}\frac{X_n\times M_n}{M_n}

now multiplying every coordinate x by the mass of each object (romeo, juliet and the boat) and dividing all by the total mass  taking by reference the position of juliet.

X_{cm}=\frac{53\times0 +81\times2.7+79\times1.35}{53+81+79}

X_cm = 1.4589 m

When the forces involved are internals, the center of mass don't change  

After the movement the center of mass remains in the same distance from the shore, but change relative to the rear of the boat.

X_{cm}=\frac{79\times1.35+(81+53)\times2.7}{53+81+79}

X_cm= 2.10 m

this displacement is how the boat move toward the shore.

2.10-1.46= 0.64 m

5 0
3 years ago
What is a conclusion?
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The end or finish of an event or process.
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