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GaryK [48]
3 years ago
15

Suppose that a 1000 kg car is traveling at 25 m/s (aprox 55mph). Its brakes can apply a force of 5000N. What is the minimum dist

ance required for the car to stop?
Physics
2 answers:
Brrunno [24]3 years ago
8 0

Assuming the the car is travelling to the right (→):

R(\rightarrow), F = ma

\implies a =  \frac{F}{m}

=  \frac{-5000}{1000}

= -5 \ ms^{-2}

The information we know:

u = 25 \ ms^{-1}

v = 0

a = -5 \ ms^{-2}

Using one of the equations of motion:

v^2 = u^2 + 2as

\implies s = \frac{v^2 -u^2}{2a}

=  \frac{0^2 - 25^2}{2\times (-5)}

=  \frac{625}{10}

= 62.5\ m

Mademuasel [1]3 years ago
5 0

62.5 m

<h3>Further explanation</h3>

<u>Given:</u>

  • A 1000 kg car is traveling at 25 m/s (approx 55 mph).  
  • Its brakes can apply a force of 5000 N.  

<u>Question:</u>

What is the minimum distance required for the car to stop?

<u>The Process:</u>

Newton's second law of motion: \boxed{ \ \Sigma F = ma \ }

The car is said to experience braking force in the opposite direction to the car's movement. We will find out the amount of acceleration due to braking. In this issue, it is more precisely called deceleration.

\boxed{ \ \Sigma F = ma \ } \rightarrow \boxed{ \ a = \frac{- friction \ force}{m} \ }

The minus sign on the frictional force indicates the opposite direction to the object motion.

\boxed{ \ a = \frac{- 5000}{1000} \ } \rightarrow \boxed{ \ a = - 5 \ m/s^2 \ }

The minus sign emphasizes the acceleration in the form of deceleration. The car will stop after traveling a certain distance which we will find out.

Next, let us use one of the following equations of uniform motion.

\boxed{ \ v^2 = u^2 + 2ad \ }

  • v = final velocity → v = 0 m/s
  • u = initial velocity → u = 25 m/s
  • a = - 5 m/s²
  • d = distance travelled

Let us calculate the minimum distance required for the car to stop.

0² = 25² + 2(-5)(d)

10d = 625

\boxed{d = \frac{625}{10}}

Thus, the minimum distance required for the car to stop is 62,5 m.

- - - - - - - - - -

Alternative Steps

We can also use the relationship between work and the change in kinetic energy (ΔKE).

Recall that,

  • work done (W) = force x distance,
  • kinetic \ energy = \frac{1}{2}mv^2
  • and W = ΔKE.

Let us calculate the minimum distance required for the car to stop.

\boxed{ \ W = \Delta KE \ }

\boxed{ \ -f \times d = \frac{1}{2}m(v^2 - u^2) \ }

The minus sign on the frictional force indicates the opposite direction to the object motion.

\boxed{ \ -5000 \times d = \frac{1}{2}(1000)(0^2 - 25^2) \ }

\boxed{ \ -5000 \times d = (500)(-625) \ }

\boxed{ \ d = \frac{(500)(-625)}{-5000} \ }

\boxed{ \ d = \frac{625}{10} \ }

Thus, the minimum distance required for the car to stop is 62,5 m.

<h3>Learn more</h3>
  1. A case problem of uniformly accelerated motion and Newton's Second Law brainly.com/question/11181200
  2. Finding the acceleration between two vectors brainly.com/question/6268248
  3. Determine the flea's acceleration brainly.com/question/5424148

Keywords: friction forces, brakes, travelling, the minimum distance, Newton's Second Law, work, kinetic energy, velocity, uniformly accelerated motion, acceleration

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Answer with Explanation:

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Resistance of solenoid,R=4.3 ohm

Magnetic field,B=3.7\times 10^{-2} T

Current,I=4.6 A

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Radius of wire,r=\frac{d}{2}=\frac{0.5\times 10^{-3}}{2}=0.25\times 10^{-3} m

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Radius of solenoid,r'=1 cm=1\times 10^{-2} m

1 cm=10^{-2} m

Resistivity of copper,\rho=1.68\times 10^{-8}\Omega m

We know that

R=\frac{\rho l}{A}

Where A=\pi r^2

Using the formula

4.3=\frac{1.68\times 10^{-8}\times l}{\pi(0.25\times 10^{-3})^2}

l=\frac{4.3\times \pi(0.25\times 10^{-3})^2}{1.68\times 10^{-8}}=50.23 m

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Number of turns of wire=\frac{50.26}{2\pi(1\times 10^{-2}}=800

Hence, the number of turns of the  solenoid,N=799

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3.7\times 10^{-2}=4\pi\times 10^{-7} n\times 4.6

n=\frac{3.7\times 10^{-2}}{4\times 3.14\times 10^{-7}\times 4.6}

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L=\frac{N}{n}

L=\frac{799}{6404}

L=0.125 m=0.125\times 100=12.5 cm

Length of solenoid=12.5 cm

1m=100 cm

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