Force contribution while pushing box | Vectors | Precalculus | Khan Academy

TL;DR

Analyzing the forces and components of two individuals pushing a box towards a target reveals the magnitude of force exerted by each person and the total force in the desired direction.

Transcript

Voiceover: Let's say that you have two folks that are trying to collectively push a box across the snow towards a target, so this is where the box is, right over here and this is the target, right over here. Let me write that, that is the target. That's where they're trying to get the box, and person A, because for some reason, they can't push it f... Read More

Key Insights

• 🎯 Two individuals exert forces on a box to move it towards a target, but they cannot push directly towards the target due to various reasons.
• 🧑 The forces exerted by each person can be broken down into components in the direction of the target using trigonometric functions.
• 😘 Person B, despite having a lower force magnitude, contributes more force towards the target due to their larger force component in that direction.

Questions & Answers

Q: How can we determine the force exerted by each person in the direction of the target?

To find the force in the desired direction, we calculate the component of each person's force using trigonometric functions. Person A's force component is 270 newtons, while Person B's force component is approximately 290 newtons.

Q: Who is exerting more force towards the target, Person A or Person B?

Although Person B's force magnitude is less than Person A's, their force component towards the target is greater. Person B is exerting about 19.5 newtons more force in the desired direction.

Q: What is the total force pushing the box towards the target?

The total force pushing the box towards the target is the sum of the force components of Person A and Person B, which is approximately 560 newtons.

Q: What impacts the direction and magnitude of the forces exerted by Person A and Person B?

Factors such as solid footing and the softness of the box affect the direction and magnitude of the forces exerted by Person A and Person B. These factors require both individuals to push at angles away from the direct line towards the target.

Summary & Key Takeaways

• Two people are pushing a box towards a target, but unable to push directly towards it due to various reasons.

• Person A exerts a force of 330 newtons at a 35-degree angle, while person B exerts a force of 300 newtons at a 15-degree angle.

• By calculating the components of their forces in the direction of the target, it is found that person B contributes more force towards the target, with a difference of approximately 19.5 newtons. The total force in the desired direction is 560 newtons.