# What's the Total Force Exerted on the Skater?

• Austin Gibson
In summary, the question involves calculating the total force exerted on a 65.0-kg ice skater being pushed by two others with forces of 21N and 36N. The solution involves finding the components of the forces and adding them together, resulting in a final vector of 33.84i + 24.35j. The axes in the figure are labeled as X and Z, and it is important to pay attention to the direction of the positive Z axis.
Austin Gibson

## Homework Statement

"Consider the 65.0-kg ice skater being pushed by two others as shown in the figure below."
Figure: https://gyazo.com/9d7525071f54b00ea7e720abdeb50594

Find the total force exerted on her by the others, given that F1 = 21N and F2 = 36N. Express your answer in vectorm form.

## Homework Equations

I doubt "F=ma" is relevant for this question considering we're merely calculating the force directed towards the skater instead of her movement thereafter.

## The Attempt at a Solution

I calculated the components of F1 and F2 with the following numbers:
I judged the angle of F1 to be (360 - 24 = 336).
F1: 21cos336 (x-component) + 21sin336 (y-component).
I judged the angle of F2 to be (90 - 24 = 66).
F2: 36cos66 (x-component) + 36sin66 (y-component).
I calculated the sum of these as 33.84i + 24.35j.
Judging by the picture, are my translations of the angles correct?
Any guidance is appreciated.

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Yes, your analysis of the angles is correct and thus your expressions for the components of ##F_1## and ##F_2## are correct. I haven't checked the numerical calculation but I always consider that to be a small part of the solution.

The axis appear to be labeled X , Z rather than X, Y.

Austin Gibson
CWatters said:
The axis appear to be labeled X , Z rather than X, Y.
Well spotted. And notice the direction of +Z axis

CWatters and Austin Gibson
Aha! That was mildly clumsy of me. I apologize. I appreciate your keen eyes. With this new information, I will redo my calculations. Thank you for your contributions.

gneill

## 1. What is the total force exerted on the skater?

The total force exerted on a skater is the sum of all the forces acting on them. This includes the force of gravity, the normal force from the surface they are skating on, and any other external forces such as air resistance or friction.

## 2. How is the total force calculated?

The total force is calculated using Newton's Second Law of Motion, which states that force is equal to mass multiplied by acceleration. In the case of a skater, the total force can be calculated by multiplying the skater's mass by their acceleration, which is the rate at which their velocity changes.

## 3. Can the total force change?

Yes, the total force on a skater can change depending on various factors such as the skater's speed, direction, and the surface they are skating on. For example, if the skater speeds up or slows down, the total force will change accordingly.

## 4. Why is the total force important for a skater?

The total force is important for a skater because it determines their motion and ability to move on the surface. If the total force is too weak, the skater may not be able to overcome the force of friction and move forward. If the total force is too strong, the skater may accelerate too quickly and lose control.

## 5. How does the total force affect the skater's performance?

The total force can have a significant impact on a skater's performance. If the total force is well-balanced and allows the skater to maintain their desired speed and direction, their performance will likely be better. However, if the total force is unbalanced or too weak, it can hinder the skater's performance and make it more difficult for them to execute certain movements or tricks.

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