Understanding the Concepts
* Weight (N): Weight is the force exerted on an object due to gravity. It's related to mass (m) by the equation: Weight (W) = mass (m) * acceleration due to gravity (g). Since we're not given the mass directly, we'll need to work with the weight.
* Kinetic Energy (J): Kinetic energy is the energy an object possesses due to its motion. It's calculated using the equation: Kinetic Energy (KE) = (1/2) * mass (m) * velocity squared (v²).
Solving the Problem
1. Find the mass:
* We know Weight (W) = 1 N.
* We know the acceleration due to gravity (g) is approximately 9.8 m/s².
* Using the equation W = m * g, we can solve for mass:
* m = W / g = 1 N / 9.8 m/s² ≈ 0.102 kg
2. Use the kinetic energy equation:
* We know KE = 1 J.
* We know the mass (m) ≈ 0.102 kg.
* Let's plug these values into the kinetic energy equation and solve for velocity (v):
* 1 J = (1/2) * 0.102 kg * v²
* 1 J = 0.051 kg * v²
* v² = 1 J / 0.051 kg ≈ 19.6 m²/s²
* v ≈ √19.6 m²/s² ≈ 4.43 m/s
Therefore, the speed of the 1N weight when its kinetic energy is 1 J is approximately 4.43 m/s.
