Question

(a) Calculate the kinetic energy in joules of a 45-g golf ball moving at \(61 \mathrm{~m} / \mathrm{s}\). (b) Convert this energy to calories. (c) What happens to this energy when the ball lands in a sand trap?

Short answer

The kinetic energy of the 45-g golf ball moving at 61 m/s is approximately 83.72 joules. This energy can be converted to approximately 20.00 calories. When the golf ball lands in a sand trap, its kinetic energy is converted into heat, sound, and distributed among the sand particles as they collide and come to a stop.

Step-by-step solution

Calculate the kinetic energy

First, we need to calculate the kinetic energy of the golf ball. The formula for kinetic energy is given by: \(KE = \frac{1}{2}mv^2\) where KE is the kinetic energy, m is the mass of the object in kilograms, and v is the velocity of the object in meters per second. Given the mass of the golf ball is 45 g and the velocity is 61 m/s, we can find its kinetic energy. First, convert the mass from grams to kilograms: \(m = 45 g × \frac{1 kg}{1000 g} = 0.045 kg\) Now, we can plug the mass and velocity into the formula: \(KE = \frac{1}{2}(0.045 kg)(61 m/s)^2\)

Compute the kinetic energy

Calculate the kinetic energy by plugging in the values: \(KE = \frac{1}{2}(0.045 kg)(61 m/s)^2 = 0.0225 kg × 3721 m^2/s^2\) \(KE = 83.72375 J\) The kinetic energy of the golf ball is approximately 83.72 joules.

Convert the energy to calories

Now, we need to convert the energy from joules to calories. We know that: \(1 cal = 4.184 J\) To convert the energy to calories, we can use the following formula: \(Energy (cal) = \frac{Energy (J)}{4.184}\) Plug the value of the energy we calculated earlier: \(Energy (cal) = \frac{83.72375 J}{4.184} = 20.00407 cal\) The energy of the golf ball in calories is approximately 20.00 calories.

Energy when the ball lands in a sand trap

When the golf ball lands in a sand trap, the kinetic energy is converted into heat and sound as the golf ball comes to a stop. The sand particles in the trap collide with the golf ball and each other, causing the kinetic energy to be transferred and distributed among all particles involved. The energy is also partially absorbed by the surrounding sand and air in the form of heat, and some of the energy is released as sound during the impact.

Key concepts

Kinetic Energy Formula

The kinetic energy formula is an expression of the energy that an object possesses due to its motion. It is given by the equation:
\( KE = \frac{1}{2}mv^2 \),
where \( KE \) stands for kinetic energy, \( m \) represents the mass of the object, and \( v \) represents the velocity of the object. To ensure that the units are consistent, the mass should be expressed in kilograms (kg) and the velocity in meters per second (m/s).
In the context of the given example, the mass of the golf ball needed to be converted from grams to kilograms before we could use the formula. Calculating kinetic energy is crucial for understanding the implication of an object’s mass and velocity on its overall energy state. For students aiming to master the kinetic energy calculations, it is pertinent to remember unit conversions and to square the velocity before multiplying by the mass.

Practical Applications

• Physics problems involving moving objects
• Predictive models in engineering to calculate forces during impact
• Sports science to improve performance

Energy Conversion

Energy conversion is the process of changing one form of energy into another. In physics, it’s important to understand that energy can neither be created nor destroyed, which is a principle known as the conservation of energy. However, it can be converted from one form to another.
In the example exercise, when the moving golf ball lands in a sand trap, its kinetic energy is converted into other forms of energy, primarily heat and sound. The interactions with the sand particles convert the ball's organized kinetic energy into randomized energy distributed amongst the sand and air particles. It’s essential to grasp that during such energy conversions, the total amount of energy remains the same; it simply changes form, following the conservation law.

Common Types of Energy Conversion

• Electrical energy to mechanical energy in motors
• Chemical energy to electrical energy in batteries
• Kinetic energy to thermal energy in brakes

Work-Energy Principle

The work-energy principle is a concept in physics that states the work done on an object is equal to the change in its kinetic energy. Work and energy are both measured in joules in the International System of Units (SI). This principle is closely tied to the conservation of energy and can be stated as:
\( Work = Delta KE \),
where \( Delta KE \) is the change in kinetic energy of the object. When work is done on an object by applying a force over a distance, the object’s kinetic energy changes. This can result in an increase or decrease in the object’s velocity and therefore, its kinetic energy.
Understanding the work-energy principle helps explain how forces acting on an object influence its motion and energy. In the case of the golf ball exercise, as the ball comes to rest in a sand trap, the work done by the sand and other forces equals the loss in the ball's kinetic energy.

Real-World Examples

• Roller coasters converting potential energy to kinetic energy as they descend
• A bike slowing down as the brakes do work to convert kinetic energy to heat
• Athletes using work-energy principles to optimize their movements