Question

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name: julian smith
work, energy, and power problems

1. what is the kinetic energy of a 0.013 kg goldfinch if the bird has a speed of 8.5 m/s?

given: m = 0.013 kg, v = 8.5 m/s find: ke = ? j eqn: ke = ½ mv²

1. how much work is required for a 74 kg sprinter to accelerate from rest to a speed of 2.2 m/s?

given: m = 74 kg, v = 2.2 m/s find: ke = ? j eqn: ke = ½ mv²

1. what is the potential energy of a 79 kg person sitting on a 3.0 m high diving board?

given: m = 79 kg, g = 10 m/s², h = 3.0 m find: pe = ? j eqn: pe = mgh

1. in the work and energy lab, a cart was pulled up a ramp and the force and distance were measured.

a. if the force is 5.0 newtons and the cart travels 1.00 meters, how much work is done by your arm on the cart?
given: f = 5.0 n, d = 1.00 m find: w = ? j eqn: w = fd
b. if the work done by your arm to the cart is 5.00 joules, how much potential energy does the cart now have?
c. how much kinetic energy does the cart have when it is allowed to roll back down the ramp just before it hits the stop at the end of the track if the work done is 5.00 joules?

Explanation:

Problem 1

Step1: Identify the formula for kinetic energy

The formula for kinetic energy (KE) is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass and \( v \) is the velocity.

Step2: Substitute the given values into the formula

We are given \( m = 0.013 \, \text{kg} \) and \( v = 8.5 \, \text{m/s} \). Substituting these values into the formula:

$$ KE = \frac{1}{2} \times 0.013 \, \text{kg} \times (8.5 \, \text{m/s})^2 $$

First, calculate \( (8.5)^2 = 72.25 \). Then, multiply by \( 0.013 \): \( 0.013 \times 72.25 = 0.93925 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 0.93925 = 0.469625 \, \text{J} \).

Step1: Identify the formula for kinetic energy

The formula for kinetic energy (KE) is \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass and \( v \) is the velocity.

Step2: Substitute the given values into the formula

We are given \( m = 74 \, \text{kg} \) and \( v = 2.2 \, \text{m/s} \). Substituting these values into the formula:

$$ KE = \frac{1}{2} \times 74 \, \text{kg} \times (2.2 \, \text{m/s})^2 $$

First, calculate \( (2.2)^2 = 4.84 \). Then, multiply by \( 74 \): \( 74 \times 4.84 = 358.16 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 358.16 = 179.08 \, \text{J} \).

Step1: Identify the formula for potential energy

The formula for gravitational potential energy (PE) is \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given \( m = 79 \, \text{kg} \), \( g = 10 \, \text{m/s}^2 \), and \( h = 3.0 \, \text{m} \). Substituting these values into the formula:

$$ PE = 79 \, \text{kg} \times 10 \, \text{m/s}^2 \times 3.0 \, \text{m} $$

First, multiply \( 79 \times 10 = 790 \). Then, multiply by \( 3.0 \): \( 790 \times 3.0 = 2370 \, \text{J} \).

Answer:

The kinetic energy of the goldfinch is approximately \( 0.47 \, \text{J} \) (or \( 0.469625 \, \text{J} \)).

Problem 2