A child is at rest on a tricycle with a mass of 16.7 kilograms. A parent pushes forward with a force of 29 N for 2.62 seconds. What is the final kinetic energy (KE) of the child?
The Correct Answer and Explanation is:
To find the final kinetic energy (KE) of the child on the tricycle after being pushed, we need to first calculate the acceleration produced by the parent’s force, determine the final velocity after the pushing force has been applied, and then use that velocity to find the kinetic energy.
Step 1: Calculate the acceleration
Using Newton’s second law of motion, the formula is:
[
F = m \cdot a
]
Where:
- ( F ) is the force applied (29 N),
- ( m ) is the mass of the tricycle (16.7 kg),
- ( a ) is the acceleration.
Rearranging the formula to solve for acceleration gives:
[
a = \frac{F}{m} = \frac{29 \, \text{N}}{16.7 \, \text{kg}} \approx 1.735 \, \text{m/s}^2
]
Step 2: Calculate the final velocity
The velocity of the child after the force has been applied for a time of ( t = 2.62 ) seconds can be calculated using the formula:
[
v = a \cdot t
]
Substituting the values we calculated:
[
v = 1.735 \, \text{m/s}^2 \cdot 2.62 \, \text{s} \approx 4.55 \, \text{m/s}
]
Step 3: Calculate the final kinetic energy
The kinetic energy (KE) is given by the formula:
[
KE = \frac{1}{2} m v^2
]
Substituting in the mass and the final velocity:
[
KE = \frac{1}{2} \cdot 16.7 \, \text{kg} \cdot (4.55 \, \text{m/s})^2
]
Calculating ( v^2 ):
[
(4.55 \, \text{m/s})^2 \approx 20.7025 \, \text{m}^2/\text{s}^2
]
Now, substituting back into the KE formula:
[
KE = \frac{1}{2} \cdot 16.7 \cdot 20.7025 \approx 173.67 \, \text{J}
]
Final Answer
Thus, the final kinetic energy of the child on the tricycle after being pushed for 2.62 seconds is approximately 173.67 joules.
Conclusion
In summary, we applied Newton’s second law to determine the acceleration from the applied force, then used this acceleration to find the final velocity after a specific time. Finally, we calculated the kinetic energy using the mass of the tricycle and the final velocity. The principles of mechanics are crucial in understanding the motion of objects, particularly in how forces influence acceleration and energy.