Question

Calculate To move a suitcase up to the check-in stand at an airport, a student pushes with a horizontal force through a distance of 0.95 m. If the work done by the student is 32 J, what is the magnitude of the force he exerts?

Short answer

The magnitude of the force is approximately 33.68 N.

Step-by-step solution

Understand the Work Formula

Work done (W) by a force can be calculated using the formula: \( W = F \cdot d \cdot \cos(\theta) \). In this problem, \( W = 32 \, \text{J} \) and \( d = 0.95 \, \text{m} \). Since the force is applied horizontally, the angle \( \theta \) is 0 degrees, and \( \cos(0) = 1 \). Thus, the formula simplifies to \( W = F \cdot d \).

Rearrange the Formula to Solve for Force

We need to isolate the force (\( F \)) in the equation. From \( W = F \cdot d \), rearranging gives us \( F = \frac{W}{d} \).

Substitute Known Values into the Equation

Substitute \( W = 32 \, \text{J} \) and \( d = 0.95 \, \text{m} \) into the equation \( F = \frac{W}{d} \), which becomes \( F = \frac{32}{0.95} \).

Calculate the Magnitude of the Force

Perform the division to find \( F \). Calculating \( F = \frac{32}{0.95} \) results in \( F \approx 33.68 \, \text{N} \).

Key concepts

Force Calculation

Understanding how to calculate force is a fundamental aspect of physics. To determine the force exerted in any situation, we often use the formula for work (denoted as \( W \)) which relates work, force, and distance. This formula can be given as:

• \( W = F \cdot d \cdot \cos(\theta) \)

Work in physics is the measure of energy transferred by a force moving an object through a distance. In the case of pushing a suitcase, if the force is applied horizontally, the angle \( \theta \) between the force and the direction of motion is 0 degrees. This simplifies the equation to \( W = F \cdot d \), since \( \cos(0) = 1 \).

To find the force \( F \), rearrange the formula to \( F = \frac{W}{d} \). Simply plug in the values of work and distance to get the required force. In the original problem, \( W = 32 \) joules and \( d = 0.95 \) meters. By calculating \( F = \frac{32}{0.95} \), we find the force is approximately 33.68 newtons (N).

Knowing how to manipulate this equation is essential in many physics problems where forces and energy are involved.

Newton's Laws

Newton's laws of motion are the cornerstone of classical physics. They help us understand how forces interact with objects. Each law gives us insights into different aspects of motion.

• First Law: Law of Inertia
  If no net force acts on an object, it will continue in its state of rest or uniform motion. This law introduces the concept of inertia, which is the resistance of any physical object to change in its motion.
• Second Law: Law of Acceleration
  The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is often expressed as \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration.
• Third Law: Action and Reaction
  For every action, there is an equal and opposite reaction. This means that forces always come in pairs. If you push against a wall, it pushes back against you with equal force.

When solving physics problems such as determining the force needed to move an object, understanding Newton's laws not only helps conceptualize the situation but also aids in correctly identifying and applying the necessary equations.

Physics Problem Solving

Solving physics problems can sometimes seem daunting, but breaking them down into manageable steps makes it more approachable. Here’s a simple method you can use to effectively tackle them:1. **Understand the Problem:** Carefully read through the problem. Identify what is given and what needs to be found. Know the units for each quantity and what they represent.2. **Choose the Right Formulas:** Based on what's asked, determine which physical principles and formulas are relevant. In problems involving work and energy, key formulas often involve work \( W = F \cdot d \cdot \cos(\theta) \) or Newton's second law \( F = ma \).3. **Rearrange and Solve:** Manipulate the formulas to isolate the variable you need to solve for. Ensure units are consistent before plugging in the numbers.4. **Calculate and Check:** Perform the calculations. Double-check your math and make sure your answer makes sense contextually. Confirm that all physical principles have been appropriately considered.5. **Reflect:** After solving, take a moment to understand the significance of your answer. Reflect on how changing variables might affect the outcome.By using a structured approach to physics problem-solving, you ensure that each part of the question is addressed, helping to build confidence and accuracy in your answers.