An ice skater is gliding horizontally across the ice with an initial velocity of +6.3 m/s. The coefficient of kinetic friction between the ice and the skate blades is 0.081, and air resistance is negligible. How much time elapses before her velocity is reduced to +2.8 m/s ?
First calculate the friction force on the ice skates. Call that F
F = M g *(0.081)
The loss of forward momentum equals the impulse, F*t
M (6.3 - 2.8) = F * t = M g *0.081* t
Note that M cancels out, so you do not need to know the mass M
t = (3.5 m/s)/[0.081*9.8 m/s^2]
= 4.4 seconds
To find the time elapsed before the velocity of the ice skater is reduced, we can use the following steps:
Step 1: Calculate the acceleration caused by friction.
The frictional force can be calculated using the equation: frictional force = coefficient of kinetic friction * normal force
Since the air resistance is negligible, the normal force is equal to the weight of the skater, which can be calculated as: normal force = mass * gravity
The acceleration caused by friction can then be found using the equation: acceleration = frictional force / mass
Step 2: Calculate the deceleration rate.
Since the ice skater initially has a positive velocity and the velocity is reducing, the acceleration caused by friction would act in the opposite direction to the initial velocity. Therefore, the acceleration should be negative.
The deceleration rate can be calculated as the negative acceleration value.
Step 3: Use the equation of motion to find the time.
The equation of motion for uniformly decelerated motion is: final velocity = initial velocity + (acceleration * time)
Now, let's go ahead and calculate the time elapsed:
Step 1: Calculating the acceleration caused by friction.
The coefficient of kinetic friction is given as 0.081.
The mass of the skater is not given.
Step 2: Calculating the deceleration rate.
The acceleration caused by friction would be equal to the deceleration rate, and it should be negative since it acts in the opposite direction to the initial velocity.
Step 3: Using the equation of motion to find the time.
The initial velocity is +6.3 m/s (since it's given as "horizontally across the ice").
The final velocity is +2.8 m/s (since it's given as "reduced to +2.8 m/s").
The acceleration is the negative value of the acceleration caused by friction (from Step 2), and we'll denote it as "deceleration" in the equation.
We need to solve for the time, denoted as "t" in the equation.
Putting all the values together, we get the equation:
2.8 m/s = 6.3 m/s + (deceleration * t)
Now, we can rearrange the equation to solve for "t":
t = (2.8 m/s - 6.3 m/s) / deceleration
Please provide the value for the mass of the skater in order to proceed with the calculations.
To find the time it takes for the ice skater's velocity to be reduced to +2.8 m/s, we can use the equation of motion involving kinetic friction.
The equation that relates the acceleration due to kinetic friction (a) to the coefficient of kinetic friction (μk) and the acceleration due to gravity (g) is:
a = μk * g
In this case, since the ice skater is gliding horizontally, there is no acceleration due to gravity acting in the horizontal direction. Therefore, the acceleration due to friction is equal to the skater's deceleration.
The equation that relates acceleration (a), initial velocity (v0), final velocity (v), and time (t) is:
v = v0 + a * t
Since the ice skater is slowing down, the acceleration due to friction will be negative.
Rearranging the equation to solve for time (t), we have:
t = (v - v0) / a
Now, let's substitute the given values into the equation.
v0 = +6.3 m/s (initial velocity)
v = +2.8 m/s (final velocity)
μk = 0.081 (coefficient of kinetic friction)
To find the acceleration due to kinetic friction, we can use:
a = μk * g
Assuming the acceleration due to gravity (g) is roughly 9.8 m/s^2, we can calculate:
a = 0.081 * 9.8 ≈ 0.7998 m/s^2
Now, substitute these values into the equation to find the time:
t = (2.8 - 6.3) / (-0.7998)
Calculating this expression, we get:
t = -3.5 / (-0.7998)
Simplifying further, we have:
t ≈ +4.38 seconds
Therefore, it will take approximately 4.38 seconds for the skater's velocity to be reduced to +2.8 m/s.
Why did the ice skater go to therapy?
Because she couldn't glide through her emotional issues!