Question

A weightlifter does \(9.8 \mathrm{~J}\) of work while lifting a weight straight upward through a distance of \(0.12 \mathrm{~m}\). What was the force exerted by the weightlifter?

Short answer

The force exerted by the weightlifter is approximately 81.67 N.

Step-by-step solution

Understand the Problem

We need to find the force exerted by the weightlifter while lifting a weight. We know the work done and the distance through which the weight is lifted.

Recall the Work Formula

The formula for work done is given by \( W = F \cdot d \cdot \cos(\theta) \), where \( W \) is work, \( F \) is the force, \( d \) is the distance moved, and \( \theta \) is the angle between force and displacement direction. Here, the angle \( \theta \) is \( 0 \) degrees because the force and the displacement are in the same direction.

Simplify the Formula

Since force is exerted in the same direction as displacement, \( \cos(0) = 1 \). So, the equation simplifies to \( W = F \cdot d \).

Rearrange to Find Force

Rearrange the equation to solve for force \( F \). We have \( F = \frac{W}{d} \).

Plug in the Values

Substitute the known values into the equation: \( W = 9.8 \mathrm{~J} \) and \( d = 0.12 \mathrm{~m} \). The equation becomes \( F = \frac{9.8}{0.12} \).

Calculate the Force

Compute the value \( F = \frac{9.8}{0.12} = 81.67 \mathrm{~N} \). The force exerted by the weightlifter is \( 81.67 \mathrm{~N} \).

Key concepts

force calculation

One of the fundamentals of physics problems involves calculating forces. A force is simply a push or pull acting on an object. Forces have both magnitude and direction, making them vector quantities. When calculating force, we often rely on Newton's Second Law of Motion, which establishes a relationship between force, mass, and acceleration. However, in certain scenarios—such as this exercise—the force is calculated using the work-energy principle.

In this context, the force calculation is based on the work done by the weightlifter. Since the work done is given, and the distance is known, we can use the work formula to determine the force exerted. This is a practical application of physics principles to find the force in scenarios where the force is constant and acts over a distance.

work formula

The work formula is a pivotal concept in solving many physics problems. Work is defined as the energy transferred when a force makes an object move. The basic formula for calculating work is: \[ W = F \cdot d \cdot \cos(\theta) \] Where:
- \( W \) represents the work done (in joules),
- \( F \) is the force applied (in newtons),
- \( d \) is the distance over which the force is applied (in meters),
- \( \theta \) is the angle between the direction of the force and the direction of movement.

In our exercise, the force and direction of movement are aligned, meaning \( \theta = 0 \) degrees, and \( \cos(0) = 1 \). Therefore, the equation simplifies to: \[ W = F \cdot d \] By rearranging this equation, we can solve for force when work and distance are known: \[ F = \frac{W}{d} \] This allows us to compute the force the weightlifter exerted when given the work and the distance.

physics problems

Solving physics problems involves applying theoretical knowledge to practical situations. These problems often require a systematic approach to find a solution. It's not just about numbers; it's about understanding the relationships between different physical quantities.

Let's delve into the steps commonly followed in solving these problems:

• **Understand the problem:** Clearly identify what is being asked and what informations are provided.
• **Identify relevant physical laws or formulas:** Determine which physics concepts will help solve the problem; in this exercise, the work formula was key.
• **Substitute known values and solve:** Insert the known values into the relevant equations to find the unknown quantity.
• **Check units and ensure accuracy:** Make sure your resulting units are consistent, and verify calculations to ensure they make sense.

These steps help systematically break down a complex problem into manageable parts. In our exercise, knowing the work done and the distance enabled us to find out the force applied using logical, clear steps. This approach can be extended to a wide variety of physics problems.