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You throw a 5.5 g coin straight down at 4.0 m/s from a 25-m-high bridge.

AHow much work does gravity do as the coin falls to the water below?

B)What is the speed of the coin just as it hits the water?

Verified Answer :

smmwaite

Answer

A) 1,347.5 Joules

B) 22.49 m/s


Explanation

Part A

The work done by the gravity is known as potential energy.

It is given by;

P.E = mgh

Where m is mass, g is acceleration due to gravity and h is the vertical height.

P.E = 5.5 × 9.8 ×25

= 1,347.5 Joules.

Part B

Using the Newton's third Law of motion,

V² = U² +2as

Where v is final velocity, u is the initial velocity, and s is the displacement of the stone.

V² = 4² + (2×9.8×25)

= 16 + 490

= 506

V = √506

= 22.49 m/s


skyluke89

A) 1.35 J

Explanation:

The work done by gravity on the coin is equal to the force F applied (which is equal to the weight of the coin) times the height of the fall, d:

\(W=Fd\)

The weight of the coin is: \(F=mg=(0.0055 kg)(9.81 m/s^2)=0.054 N\)

And using d=25 m, we find the work done:

\(W=Fd=(0.054 N)(25 m)=1.35 J\)


B) 22.5 m/s

Explanation:

this is a uniformly accelerated motion, with constant acceleration g=9.81 m/s^2, so the velocity of the coin can be found by using the following SUVAT equation

\(v^2-u^2=2ad\)

where

v is the final velocity of the coin

u=4.0 m/s is the initial velocity of the coin

a=9.81 m/s^2 is the acceleration

d=25 m is the heigth of the fall

Using the equation, we find

\(v=\sqrt{u^2+2ad}=\sqrt{(4 m/s)^2+2(9.81 m/s^2)(25 m)}=22.5 m/s\)

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