Question(I) How high will a $1.85-\mathrm{kg}$ rock go if thrown straight up by someone who does 70.0 J of work on it? Neglect air resistance.

Studdy Solution

STEP 1

1. The rock has a mass of $1.85 \, \text{kg}$ .
2. The work done on the rock is $70.0 \, \text{J}$ .
3. Air resistance is neglected.
4. We need to find the maximum height the rock will reach.

STEP 2

1. Understand the relationship between work and potential energy.
2. Use the work-energy principle to set up the equation.
3. Solve for the maximum height.

STEP 3

Understand the relationship between work and potential energy.
The work done on the rock is converted into gravitational potential energy at the highest point. The formula for gravitational potential energy is:
$U = mgh$
where $U$ is the potential energy, $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height.

STEP 4

Use the work-energy principle to set up the equation.
According to the work-energy principle, the work done on the rock is equal to the change in its potential energy. Therefore, we have:
$70.0 \, \text{J} = mgh$
Substitute the known values into the equation:
$70.0 = 1.85 \times 9.81 \times h$

STEP 5

Solve for the maximum height.
Rearrange the equation to solve for $h$ :
$h = \frac{70.0}{1.85 \times 9.81}$
Calculate the value:
$h \approx \frac{70.0}{18.1485}$
$h \approx 3.86 \, \text{m}$
The maximum height the rock will reach is:
$\boxed{3.86 \, \text{m}}$

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