Question

question 7 points 2
a pendulum of mass 0.5 kg is 1.2 m above the lowest point. what is its speed at the bottom?

4.85 m/s

3.5 m/s

5.0 m/s

2.5 m/s

Explanation:

Step1: Apply Conservation of Energy

The pendulum's potential energy at height \( h \) converts to kinetic energy at the bottom. The formula for gravitational potential energy is \( PE = mgh \) and kinetic energy is \( KE=\frac{1}{2}mv^{2} \). By conservation of energy, \( mgh=\frac{1}{2}mv^{2} \). The mass \( m \) cancels out, so we solve for \( v \): \( v = \sqrt{2gh} \).

Step2: Substitute Values

Given \( g = 9.8\ m/s^{2} \) and \( h = 1.2\ m \), substitute into the formula: \( v=\sqrt{2\times9.8\times1.2} \). Calculate \( 2\times9.8\times1.2 = 23.52 \), then \( \sqrt{23.52}\approx4.85\ m/s \).

Answer:

4.85 m/s (the option corresponding to this value)