Total mechanical energy of a flying rubber ball is 2000 J. It has a velocity of 151 ms-1 and is 3.1 m above the ground. Find the mass of the ball. (2dp)
To find the mass of the ball, we can use the equation for the total mechanical energy of an object:
Total Mechanical Energy (E) = Kinetic Energy (KE) + Potential Energy (PE)
The kinetic energy of the ball is given by the equation:
KE = (1/2) * m * v^2
where m is the mass of the ball and v is its velocity.
The potential energy of the ball is given by the equation:
PE = m * g * h
where g is the acceleration due to gravity and h is the height of the ball above the ground.
Since we know the total mechanical energy (E), the velocity (v), and the height (h), we can substitute these values into the equations and solve for the mass (m).
E = KE + PE
E = (1/2) * m * v^2 + m * g * h
Simplifying the equation:
2000 J = (1/2) * m * (151 m/s)^2 + m * (9.8 m/s^2) * 3.1 m
Now we can solve for m. First, let's simplify the equation:
2000 J = (1/2) * m * (22701 m^2/s^2) + (30.38 m/s^2) * m
2000 J = 11350.5 m + 30.38 m^2/s^2 * m
2000 J = 11380.88 m^2/s^2 * m
Now, rearranging the equation to solve for m:
m^2/s^2 * m = 2000 J / 11380.88 m^2/s^2
m^3/s^2 = 0.1757 kg
m = (∛(0.1757 kg)) / s
m ≈ 0.577 kg (rounded to 2 decimal places)
Therefore, the mass of the ball is approximately 0.577 kg.