You throw a 5.5 g coin straight down at 4.0 m/s from a 25-m-high bridge.
A) How 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?
A) Mass X g X height
Change the mass into kg
(.0055) X 9.8 X 25
a. mass*g*height
b. KE at bottom= mgh+1/2 m vi^2
= m(25*9.8)+m (1/2*16)
but KE at bottom=1/2 m vf^2
so vf=sqrt (2*25*9.8 +16)
Do not forget to convert the grams to kg to get the right answer.
To answer these questions, we will need to use the concepts of work and energy.
A) To calculate the work done by gravity as the coin falls, we can use the formula for gravitational potential energy:
Potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
Given that the coin has a mass of 5.5 g, we need to convert it to kilograms by dividing by 1000:
m = 5.5 g ÷ 1000 = 0.0055 kg
The acceleration due to gravity is approximately 9.8 m/s², and the height is 25 m.
So, the potential energy of the coin at the top of the bridge is:
PE = 0.0055 kg × 9.8 m/s² × 25 m = 1.3475 J
At the bottom of the bridge, just before hitting the water, the potential energy is zero since all of it has been converted to kinetic energy (due to the work done by gravity).
Therefore, the work done by gravity can be calculated as the difference in potential energy:
Work done by gravity = PE at the top - PE at the bottom
= 1.3475 J - 0 J
= 1.3475 J
So, the work done by gravity as the coin falls to the water below is 1.3475 Joules.
B) To find the speed of the coin just as it hits the water, we can use the principle of conservation of energy. At the top of the bridge, the coin only has potential energy, and at the bottom, it has only kinetic energy.
Using the equation for kinetic energy:
Kinetic energy (KE) = 0.5 × mass (m) × velocity squared (v²)
Since the potential energy at the bottom is zero, all of the initial potential energy is converted into kinetic energy. Therefore, we can equate the initial potential energy to the final kinetic energy:
PE at the top = KE at the bottom
0.5 × m × 4.0 m/s² = 0.5 × m × v²
Simplifying the equation and solving for v:
4.0 m/s² = v²
Taking the square root of both sides gives us:
v = √(4.0 m/s²) = 2.0 m/s
So, the speed of the coin just as it hits the water is 2.0 m/s.
30m/s
A:(5.5g)(9.81m/s^2)(50m)+ 2698g*m^2/s^2
B:32m/s