Question

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

Answer 1

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

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

Answer 2

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