A force of 10 N is used to lift a 600-g ball from the ground to a height of 1.8 m, when it is let go. What is the speed of the ball when it is let go??
To find the speed of the ball when it is let go, we can use the principle of conservation of energy.
First, let's calculate the gravitational potential energy of the ball at the height of 1.8 m. The formula for gravitational potential energy is:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
The mass is given as 600 g, but we need to convert it to kilograms (kg) since the SI unit is used for acceleration due to gravity. 1 kg = 1000 g, so:
mass (m) = 600 g / 1000 = 0.6 kg
The acceleration due to gravity (g) is approximately 9.8 m/s^2.
Now, we can calculate the potential energy:
PE = 0.6 kg * 9.8 m/s^2 * 1.8 m
= 10.44 Joules
According to the conservation of energy, the potential energy gained by the ball when lifting it against gravity will be converted into kinetic energy when it is let go. The formula for kinetic energy is:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Since the ball is let go, the potential energy is fully converted into kinetic energy, so the equation becomes:
PE = KE
Let's rearrange the equation to solve for velocity:
0.5 * mass * velocity^2 = PE
velocity^2 = (2 * PE) / mass
Plugging in the known values:
velocity^2 = (2 * 10.44 J) / 0.6 kg
velocity^2 = 34.8 m^2/s^2
Finally, take the square root of both sides to find the velocity:
velocity ≈ √(34.8) ≈ 5.9 m/s
Therefore, the speed of the ball when it is let go is approximately 5.9 m/s.