Question

If the force exerted by the intern is doubled and the distance is halved, does the work done by the intern increase, decrease, or remain the same?

Short answer

The work done remains the same.

Step-by-step solution

Understanding the Formula for Work

Work can be calculated using the formula \( W = F \times d \), where \( W \) is the work done, \( F \) is the force applied, and \( d \) is the distance over which the force is applied.

Initial Conditions

Initially, let the force be \( F \) and the distance be \( d \). Therefore, the initial work \( W_0 = F \times d \).

New Conditions

The force is doubled, so the new force is \( 2F \). The distance is halved, so the new distance is \( \frac{d}{2} \).

Calculate the New Work Done

Using the new conditions, the work done is \( W_1 = (2F) \times \left( \frac{d}{2} \right) = 2F \times \frac{d}{2} = F \times d \).

Compare the Initial and New Work

Comparing \( W_0 = F \times d \) and \( W_1 = F \times d \), we see that \( W_1 = W_0 \). This means the work done remains the same.

Key concepts

Force

Force is a fundamental concept in physics that describes a push or pull on an object. This interaction causes changes in the motion of the object, whether it translates, accelerates, or maintains its state. The unit of force in the International System of Units (SI) is the Newton (N).

• Force is vector-based, meaning it has both magnitude and direction. For example, pushing a door open involves force with a specific magnitude and direction.
• In the context of work and energy, force plays a significant role since it’s a key factor in doing work on an object.
• The formula for force is given by Newton's second law: \( F = m imes a \), where \( F \) represents force, \( m \) is mass, and \( a \) is acceleration.

Force is crucial in mechanics and dynamics, influencing the energy interactions between objects. Understanding how force operates helps in calculating work.

Distance

Distance refers to the amount of space between two points. In physics, it determines how far an object travels, which is essential when calculating work. Unlike displacement, which considers direction, distance is a scalar quantity, meaning only magnitude is taken into account.

• Distance comes into play in the formula for work—it is the path over which the force acts.
• The SI unit for distance is the meter (m).
• If the distance over which a force is applied changes, it directly affects the work done. For instance, in our problem set, halving the distance while doubling force maintained the same amount of work.

Accurately measuring distance is crucial, as even small changes can alter the work calculations significantly.

Formula for Work

The formula for work is a simple yet powerful tool in understanding how force affects motion over a specific distance. Work is computed by the equation \( W = F \times d \), where \( W \) represents work, \( F \) is force, and \( d \) is distance.

• Work is measured in Joules (J), with one Joule equivalent to one Newton-meter.
• If the force applied or the distance changes, the amount of work done can increase, decrease, or remain the same; it depends on how these two factors interact.
• In scenarios like the one presented in the original exercise, understanding work helps explain energy transfer in situations where force and distance vary.
• Through doubling force and halving distance, the interplay of these variables showed that work remained unchanged—counterintuitive but true when applied correctly.

Grasping the formula for work helps in predicting and calculating the energy needed or produced by moving objects.