Question

What potential energy is acquired by a hammer with a mass of 0.75 kg when raised 0.35 m?



(1 point)
Responses

2.58 joules

0.2625 joules

2.14 joules

0 Newtons

2.34 Newtons

Answer 1

The potential energy (PE) acquired by an object raised to a height can be calculated using the formula:

\[
PE = mgh
\]

where:
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

Given:
- \( m = 0.75 \, \text{kg} \)
- \( h = 0.35 \, \text{m} \)
- \( g \approx 9.81 \, \text{m/s}^2 \)

Now, plug these values into the formula:

\[
PE = 0.75 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.35 \, \text{m}
\]

Calculating it step by step:

1. First calculate \( 9.81 \times 0.35 \):
\[
9.81 \times 0.35 \approx 3.4335
\]

2. Now, multiply by the mass:
\[
PE \approx 0.75 \, \text{kg} \times 3.4335 \approx 2.575125 \, \text{J}
\]

Rounding to two decimal places gives:

\[
PE \approx 2.58 \, \text{joules}
\]

Thus, the potential energy acquired by the hammer is approximately **2.58 joules**.