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3 years ago

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The suspension cable of a 1,000 kg elevator snaps, sending the elevator moving downward through its shaft. The emergency brakes

of the elevator stop the elevator shortly before it reaches the bottom of the shaft. If the elevator fell a distance of 100 m starting from rest, the heat that the brakes must dissipate to bring the elevator safely to rest is (A) 100 J (B) 1,000 J (C) 10,000 J (D) 100,000 J (E) 1,000,000 J

1 answer:

tester [92]3 years ago

4 0

Answer:

option (E) 1,000,000 J

Explanation:

Given:

Mass of the suspension cable, m = 1,000 kg

Distance, h = 100 m

Now,

from the work energy theorem

Work done by the gravity = Work done by brake

or

mgh = Work done by brake

where, g is the acceleration due to the gravity = 10 m/s²

or

Work done by brake = 1000 × 10 × 100

or

Work done by brake = 1,000,000 J

this work done is the release of heat in the brakes

Hence, the correct answer is option (E) 1,000,000 J

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1 year ago

Two kids are playing on a newly installed slide, which is 3 m long. John, whose mass is 30 kg, slides down into William (20 kg),

yuradex [85]

Answer:

$v=3.564\ m.s^{-1}$

$\Delta v =2.16\ m.s^{-1}$

Explanation:

Given:

mass of John, $m_J=30\ kg$

mass of William, $m_W=30\ kg$

length of slide, $l=3\ m$

(A)

height between John and William, $h=1.8\ m$

<u>Using the equation of motion:</u>

$v_J^2=u_J^2+2 (g.sin\theta).l$

where:

v_J = final velocity of John at the end of the slide

u_J = initial velocity of John at the top of the slide = 0

Now putting respective :

$v_J^2=0^2+2\times (9.8\times \frac{1.8}{3})\times 3$

$v_J=5.94\ m.s^{-1}$

<u>Now using the law of conservation of momentum at the bottom of the slide:</u>

<em>Sum of initial momentum of kids before & after collision must be equal.</em>

$m_J.v_J+m_w.v_w=(m_J+m_w).v$

where: v = velocity with which they move together after collision

$30\times 5.94+0=(30+20)v$

$v=3.564\ m.s^{-1}$ is the velocity with which they leave the slide.

(B)

frictional force due to mud, $f=105\ N$

<u>Now we find the force along the slide due to the body weight:</u>

$F=m_J.g.sin\theta$

$F=30\times 9.8\times \frac{1.8}{3}$

$F=176.4\ N$

<em><u>Hence the net force along the slide:</u></em>

$F_R=71.4\ N$

<em>Now the acceleration of John:</em>

$a_j=\frac{F_R}{m_J}$

$a_j=\frac{71.4}{30}$

$a_j=2.38\ m.s^{-2}$

<u>Now the new velocity:</u>

$v_J_n^2=u_J^2+2.(a_j).l$

$v_J_n^2=0^2+2\times 2.38\times 3$

$v_J_n=3.78\ m.s^{-1}$

Hence the new velocity is slower by

$\Delta v =(v_J-v_J_n)$

$\Delta v =5.94-3.78= 2.16\ m.s^{-1}$

8 0

3 years ago

Define impulse and momentum.<br>No spam

Doss [256]

Impulse: a certain amount of force you apply for an amount of time.

Impulse: F*t where F= Force & t=time

Momentum: increasing forward motion.

A ball rolling down a slide gains momentum

p=mv where m=mass and v=velocity

Hope it helps!

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2 years ago

A 55 kg track and field athlete has an average power output of 5.4 kW during the 200 meter dash. How quickly did she finish the

olga_2 [115]

The time taken for the athlete to finish the race is 20 s (Option A)

<h3>What is power? </h3>

Power is simply defined as the rate at which work is done. It can be expressed mathematically as

Power (P) = work (W) / time (t)

But

Work = weight × distance

Therefore,

Power = (weight × distance ) / time

<h3>How to determine the time </h3>

Mass (m) = 55 Kg
Acceleration due to gravity (g) = 9.8 m/s²
Weight = mg = 55 × 9.8 = 539 N
Power (P) = 5.4 KW = 5.4 × 1000 = 5400 W
Distance (d) = 200 m
Time (t) =?

Power = (weight × distance ) / time

5400 = (539 × 200) / t

5400 = 107800 / t

Cross multiply

5400 × t = 107800

Divide both side by 5400

t = 107800 / 5400

t = 20 s

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