A ball of mass 0.1kg is thrown vertically upwards with a speed of 10ms ^ -1 from the top of a tower 10m high…

Analysis

To solve this problem, we apply the Law of Conservation of Mechanical Energy. This law states that in the absence of air resistance, the total mechanical energy of an object remains constant throughout its motion. Therefore, the total energy at the top of the tower is equal to the total energy just before the ball hits the ground.

Concept

Total Mechanical Energy ($E_T$) is the sum of Kinetic Energy ($K.E.$) and Potential Energy ($P.E.$):

• Kinetic Energy ($K.E.$) = $\frac{1}{2}mv^2$
• Potential Energy ($P.E.$) = $mgh$

Where:

• $m$ = mass (0.1 kg)
• $v$ = velocity (10 m/s)
• $g$ = acceleration due to gravity (10 m/s²)
• $h$ = height (10 m)

Solution

We calculate the total energy at the point of release (the top of the tower):

1. Calculate Kinetic Energy ($K.E.$): $$K.E. = \frac{1}{2} \times 0.1 \times (10)^2$$ $$K.E. = 0.5 \times 0.1 \times 100$$ $$K.E. = 5\text{ J}$$

2. Calculate Potential Energy ($P.E.$): $$P.E. = mgh$$ $$P.E. = 0.1 \times 10 \times 10$$ $$P.E. = 10\text{ J}$$

3. Calculate Total Energy ($E_T$): $$E_T = K.E. + P.E.$$ $$E_T = 5\text{ J} + 10\text{ J}$$ $$E_T = 15\text{ J}$$

Since energy is conserved, the total energy just before hitting the ground is the same as the total energy at the start.

Conclusion

The total energy of the ball is 15J. This matches option C.

Exam Tip

In physics problems involving "neglecting air resistance," always look for the point where you have all the necessary values (mass, height, and velocity) to calculate the total energy. Once you find the total energy at that point, you don't need to perform complex calculations for the final position—the energy remains the same!