a 0.180 kg ball falls 2.5m. How much work does the force of gravity do on the ball?
To calculate the work done by the force of gravity on the ball, we can use the equation:
Work = Force × Distance × Cosine(θ)
In this case, the force of gravity can be calculated using the formula:
Force = Mass × Acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Therefore, the force of gravity on the ball can be calculated as follows:
Force = Mass × Acceleration due to gravity
= 0.180 kg × 9.8 m/s^2
Next, we need to find the angle between the force of gravity and the direction of motion, which is vertically downward. Since the force of gravity acts downward and the ball falls vertically, the angle (θ) between them is 0 degrees.
Now we have all the information we need to calculate the work:
Work = Force × Distance × Cosine(θ)
= (0.180 kg × 9.8 m/s^2) × 2.5 m × Cosine(0°)
The cosine of 0° is 1, so the equation simplifies to:
Work = (0.180 kg × 9.8 m/s^2) × 2.5 m × 1
Calculating the result gives:
Work = 0.441 J
Therefore, the force of gravity does 0.441 Joules (J) of work on the ball as it falls 2.5 meters.