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3 years ago

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A motor vehicle has a mass of 1.8 tonnes and its wheelbase is 3 m. The centre of gravity of the vehicle is situated in the centr

al plane 0.9 m above the ground and 1.7 m behind the front axle. When moving on the level at 90 km/h the brakes applied and it comes to a rest in a distance of 50 m.
Calculate the normal reactions at the front and rear wheels during the braking period and the least coefficient of friction required between the tyres and the road. (Assume g = 10 m/s2)

1 answer:

Sergeeva-Olga [200]3 years ago

4 0

Answer:

normal reaction, front: 11,175 N
normal reaction, rear: 6,825 N
minimum coefficient of friction: 0.625

Explanation:

The speed in meters per second is ...

(90 km/h)(1000 m/km)(1 h/(3600 s)) = 25 m/s

The braking acceleration can be found from ...

a = v²/(2d) = (25 m/s)²/(2×50 m) = 6.25 m/s²

Then the braking force is ...

F = Ma = (1800 kg)(6.25 m/s²) = 11,250 N

The torque on the center of gravity is ...

T = (11,250 N)(0.90 m) = 10,125 N·m

__

If we let x and y represent the normal forces on the front and rear wheels, respectively, then we have ...

x + y = (10 m/s²)(1800 kg) = 18000 . . . . . newtons

1.7x -1.3y = 10,125 . . . . . . . . . . . . . . . . . . . newton-meters

The latter equation balances the torque due to the wheel normal forces with the torque due to braking forces.

Multiplying the first equation by 1.3 and adding that to the second, we have ...

3.0x = (1.3)(18,000) + 10,125

x = 33,525/3 = 11,175 . . . . . . . . . . . newtons normal force on front tyres

y = 18000 -11175 = 6,825 . . . . . . . .newtons normal force on back tyres

The least coefficient of friction is the ratio of horizontal to vertical acceleration, 6.25/10 = 0.625.

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Contents

1 Definitions in American context

2 History

2.1 Faster inter-city trains: 1920–1941

2.2 Post-war period: 1945–1960

2.3 First attempts: 1960–1992

2.4 Renewed interest: 1993–2008

2.5 Plans for 2008–2013

3 Current state and regional efforts

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3.1.1.1 Proposed routes

3.1.2 Northeast Maglev proposal

3.1.3 New Jersey–New York City upgrades

3.1.4 New York

3.1.5 Pennsylvania

3.2 Western States

3.2.1 California

3.2.2 Pacific Northwest

3.2.3 Arizona

3.3 Mid-Atlantic and the South

3.3.1 Florida

3.3.2 Southeast

3.3.3 Texas

3.4 Midwest

3.4.1 Illinois and the Midwest

3.5 The Southwest

4 Federal high-speed rail initiatives

4.1 American Recovery and Reinvestment Act of 2009

4.1.1 Strategic plan

4.2 2009 federal grant funding

4.3 2010 allocation

4.3.1 Cancellation of funds for Wisconsin, Ohio, and Florida

4.4 2011 and 2012 proposals and rejections of funding

5 See also

6 Notes

7 Further reading

8 External links

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