Speed Calculation Using Kinetic Energy
The problem asks for the speed of a body given its mass and kinetic energy. We are provided with the following information:
- Mass of the body, \(m = 4 \text{ kg}\)
- Kinetic Energy, \(KE = 72 \text{ J}\)
The relationship between kinetic energy, mass, and speed is defined by the kinetic energy formula:
\( KE = \frac{1}{2}mv^2 \)
To determine the speed (\(v\)), we need to rearrange this formula.
Calculating the Speed
Follow these steps to find the speed:
- Isolate \(v^2\) in the formula: Multiply both sides by 2 and divide by \(m\).
\( v^2 = \frac{2 \times KE}{m} \)
- Substitute the given values for \(KE\) and \(m\):
\( v^2 = \frac{2 \times 72 \text{ J}}{4 \text{ kg}} \)
- Simplify the expression:
\( v^2 = \frac{144 \text{ J}}{4 \text{ kg}} \)
\( v^2 = 36 \frac{\text{J}}{\text{kg}} \)
Recall that \(1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2\). Thus, the units simplify to \(\text{m}^2/\text{s}^2\).
\( v^2 = 36 \text{ m}^2/\text{s}^2 \)
- Find the speed (\(v\)) by taking the square root:
\( v = \sqrt{36 \text{ m}^2/\text{s}^2} \)
\( v = 6 \text{ m/s} \)
The calculated speed of the body is 6 m/s.
Similar Questions
- In which of the following mentioned activities is the potential energy (P.E.) converted into kinetic energy (K.E.)?
Important Questions from Work and Energy
The founder of the Pala empire was:
- A $40$ kg object is moved horizontally from point A to point B on a table. What is the work done by gravity during this movement?
- An object of mass $8$ kg is placed $7$ meters above the ground. What is the energy it possesses? (Take $g=10$ $m/s^2$)
- Raising an object from the ground results in the storage of which type of energy?
- At time t=0, a body of mass 1 Kg starts to fall freely from rest from a height of 100 m. Compared to the kinetic energy at 3 seconds, the kinetic energy at 4 seconds ________.
