# Solving Force and Rest with a Skater on Ice

• enantiomer1
In summary, the problem involves a skater of mass 68.5 kg moving at an initial velocity of 2.40 m/s on rough ice. The skater comes to a uniform stop in 3.52 seconds due to friction from the ice. The equation F=ma is needed to solve the problem, but the given variable is time instead of distance. After realizing that acceleration is equal to velocity divided by time, the solution becomes more clear.
enantiomer1

## Homework Statement

here's the problem
A 68.5 kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice.

F= ma

## The Attempt at a Solution

I'm sure this equation is reliant on finding the acceleration, but I really don't know how to do that when time (instead of distance) is our given variable
anyone know what I'm missing?

okay sorry scratch that I just had a brain fart or something -.-
obviously a= m/s2 so there for all I had to do was divide the velocity by the time
I swear to god I'm getting stupider sometimes

Your approach to the problem is correct. In order to solve for the force of friction, we need to first find the acceleration of the skater. This can be done by using the equation F = ma, where F is the force of friction, m is the mass of the skater, and a is the acceleration.

To find the acceleration, we can use the equation a = (vf - vi)/t, where vf is the final velocity (in this case, 0 m/s since the skater comes to rest) and vi is the initial velocity (2.40 m/s). Substituting in the given values, we get a = (0 - 2.40 m/s)/3.52 s = -0.68 m/s^2.

Now, we can use the equation F = ma to find the force of friction. Substituting in the mass of the skater (68.5 kg) and the acceleration we just calculated (-0.68 m/s^2), we get F = (68.5 kg)(-0.68 m/s^2) = -46.58 N.

Therefore, the force of friction acting on the skater is -46.58 N, which is the force that causes the skater to come to rest in 3.52 s.

## 1. How does friction affect a skater's movement on ice?

Friction is the force that opposes motion between two surfaces. In the case of a skater on ice, the friction between the skates and the ice surface can either increase or decrease the skater's movement. When the skater pushes off with their skates, the friction between the blades and the ice causes them to move forward. However, if the skater is not pushing off with enough force, the friction can slow down their movement.

## 2. What is the relationship between force and acceleration for a skater on ice?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the more force a skater applies, the greater their acceleration will be. Therefore, by applying a greater force with their skates, a skater can increase their acceleration on the ice.

## 3. How does the skater's body position affect their motion on the ice?

The position of a skater's body can greatly impact their motion on the ice. By leaning their body forward, a skater can reduce their air resistance and increase their speed. On the other hand, leaning backward can increase air resistance and slow down their movement. Additionally, by crouching down, a skater can lower their center of mass and increase their stability on the ice.

## 4. What is the role of inertia in a skater's movement on ice?

Inertia is the resistance of an object to change its state of motion. In the case of a skater on ice, their inertia can work to their advantage by allowing them to maintain their speed and direction once they are in motion. However, it can also make it more difficult for them to change their direction or stop completely, as they must overcome their inertia.

## 5. How does the surface area of a skater's skates affect their motion on ice?

The surface area of a skater's skates can impact their motion on ice in several ways. A larger surface area can provide more friction and allow for better control and stability on the ice. However, it can also increase air resistance and slow down their movement. On the other hand, a smaller surface area can reduce air resistance and increase speed, but it may also make it more difficult to maintain balance on the ice.

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