a skater with an initial speed of 7.60m/s is gliding across the ice. air resistance is negligible. (a)the coefficient of kinetic friction between the ice and the skate blades is 0.100. find the deceleration caused by kinetic friction. (b)how far will the skater travel before coming to rest?

someone had showed me something like this:
If the kinetic friction coeffient is 0.1, the force that is opposig motion is (F = 0.1 * M g).

(a) The deceleration rate is therefore
a = F/M = 0.1 g = 0.98 m/s^2

(b) The time to come to rest, T, is given by
a T = 7.6 m/s.
Solve for T

but i don't really understand how did he get the part : a = F/M = 0.1 g = 0.98 m/s^2

can anyone please give me some hints to do it or explain it to me? THANKS A LOT!

F=ma mew(Fn) N=W

a=f/m
a=mew(Fn)/m mew=coefficient of friction
a=mew(W)/m
a=mew(mg)/m
a= mew(g)
a=(0.100)(9.8)
a=0.980m/s^2

Since Newton's second law says F = Ma, than a = F/m.

g is the acceleration of gravity, 9.8 m/s^2

I hope that explains what I wrote earlier

so what do you mean by 0.1g?

0.1 g is g/10

I got it by using the formul a = F/M
I had already shown you that F = 0.1 M g

for b) the question is how FAR will it travel not long... so the answer is 29.4m

Well, let me break it down for you in my own clownish way!

First, let's tackle part (a). The force of kinetic friction can be calculated using the formula: F = μk * N, where μk is the coefficient of kinetic friction and N is the normal force. In this case, the normal force is equal to the weight of the skater, which is given by M * g, where M is the mass of the skater and g is the acceleration due to gravity.

So, the force of kinetic friction can be written as: F = μk * M * g. The deceleration caused by this force is given by a = F / M (Newton's second law). Substituting in the equation for the force, we get: a = (μk * M * g) / M. The mass (M) cancels out, leaving us with a = μk * g.

Now, the coefficient of kinetic friction is given as 0.1 and the acceleration due to gravity is approximately 9.8 m/s^2. Plugging in these values, we get: a = 0.1 * 9.8 = 0.98 m/s^2.

For part (b), we need to find the time it takes for the skater to come to rest. We can use the equation v = u + a * t, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 0 because the skater comes to rest. The initial velocity (u) is given as 7.6 m/s, and the acceleration (a) is -0.98 m/s^2 (negative because it's deceleration).

Plugging in these values to the equation, we get: 0 = 7.6 + (-0.98) * t. Solving for t, we find the time it takes for the skater to come to rest.

I hope that clears things up for you!

To understand how the equation a = F/M = 0.1g = 0.98 m/s^2 was obtained, let's break it down step by step:

Step 1: Understanding the equation for force due to kinetic friction
The force of kinetic friction can be calculated using the equation F = μk * N, where μk is the coefficient of kinetic friction and N is the normal force. In this case, air resistance is negligible, so the normal force is equal to the weight of the skater. Therefore, N = mg, where m is the mass of the skater and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Step 2: Calculating the force due to kinetic friction
Substituting the values in the equation, F = μk * N = μk * mg. Since the coefficient of kinetic friction μk is given as 0.100, we have F = 0.100 * mg.

Step 3: Equating force to mass times acceleration
According to Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the force opposing motion is the force due to kinetic friction (F = 0.100 * mg). Therefore, we can write 0.100 * mg = ma.

Step 4: Solving for acceleration
Rearranging the equation, we get:
a = (0.100 * mg) / m = 0.100g

Since the mass m cancels out, we are left with a = 0.100g. Plugging in the value of acceleration due to gravity g (approximately 9.8 m/s^2), we get:
a = 0.100 * 9.8 = 0.98 m/s^2

So, the deceleration caused by kinetic friction is 0.98 m/s^2.

I hope this explanation helps you understand how the equation for deceleration was obtained.