Question

A constant force of \(40.0 \mathrm{~N}\) is needed to keep a car traveling at constant speed as it moves \(5.00 \mathrm{~km}\) along a road. How much work is done? Is the work done on or by the car?

Short answer

Answer: The work done on the car is 200,000 Joules.

Step-by-step solution

Identify the given parameters

We are given the following parameters: - Constant force, F = 40.0 N - Distance traveled by the car, d = 5.00 km (We need to convert it to meters.)

Convert distance to meters

Since 1 km = 1000 m, we convert the distance to meters: 5.00 km * 1000 = 5000 m

Calculate the work done

Now that we have the force and the distance in the same unit (N, m), we can apply the formula for calculating the work done: W = F x d x cos(θ) As the direction of the force is along the road (in the same direction as the distance), θ = 0 degrees, and cos(θ) = 1. Thus, the formula becomes: W = F x d Putting the given values into the formula, we get: W = (40.0 N) x (5000 m) = 200,000 J (Joules) So, the work done is equal to 200,000 Joules.

Determine whether the work is done on or by the car

Since the force is needed to keep the car moving at a constant speed, this means the force is acting against some resistive forces like air resistance and friction. Therefore, the work is done on the car by an external force to keep it moving. In conclusion, the work done is 200,000 Joules, and it is done on the car.

Key concepts

Constant Force

In physics, a constant force refers to a force that remains fixed in both magnitude and direction over time. When a constant force is applied to an object, the object either accelerates at a steady rate or moves at a constant speed if the force is balanced by other opposing forces. In the context of our car example, a constant force of 40.0 Newtons (N) is used to maintain a uniform velocity, indicating that it counteracts other forces precisely to prevent acceleration or deceleration.

This concept is important because it simplifies calculations by allowing us to use straightforward linear equations to determine quantities like work done, which is the product of the force applied and the distance traveled in the direction of the force. The constant nature of the force means that the theorized work done will not change over the distance the force is applied.

Distance Conversion

Distance conversion is a necessary step in solving physics problems where units of measurement differ. In many situations, including our car problem, we need to convert kilometers to meters because the standard unit of distance in physics equations is the meter (m).

To convert kilometers to meters, you multiply by 1000 because one kilometer is equivalent to 1000 meters (1 km = 1000 m). It's crucial to convert distances to consistent units before calculating physical quantities like work, energy, or speed, to avoid miscalculations. For the car traveling 5.00 kilometers, the distance must be converted to 5000 meters to be used in the formula for work done. Ensuring proper units is fundamental for accurate results in physics equations.

Work-Energy Principle

The work-energy principle is a core concept in physics that relates the work done on an object to the change in its kinetic energy. The principle states that the work done by the forces acting on an object results in a change in the object's kinetic energy.

In our car exercise, however, the car moves at a constant speed, implying that there is no change in kinetic energy. The work done by the external force does not lead to acceleration; rather, it balances the resistive forces like friction and air resistance to maintain the car's velocity. This equilibrium means that all the work done by the force is used to overcome these resistive factors, which is why we can say the work is done on the car to keep it in motion. Understanding this principle helps in comprehending the relationship between force, motion, and energy.

Resistive Forces

Resistive forces are forces that oppose the motion of an object. Common examples include friction and air resistance. In the scenario with the car, even though it's moving at a constant speed, resistive forces are continually at play, working against its motion.

To maintain a steady speed, an external force must be applied to counteract these resistive forces. This does not increase the car's speed; instead, it allows the car to keep moving forward at the same rate, effectively 'using up' the energy provided by the force in doing work against resistance. Hence, when work is done in such a context, it's important to recognize that it's not about altering the speed but sustaining the motion in the presence of resistive forces.