A 75 kg water skier is pulled by a horizontal tow rope. She goes from rest to 6.0 m/s in 4.5 s when the rope's tension is 140 N. What is the magnitude of the friction force between her skis and the water?
I really dont know where to start, can someone please help :)
in the absence of friction,
F = ma, so she would only need 75*(6/4.5) = 100N
so the rest (40N) is friction
Well, let me give it a shot!
Why did the water skier bring a towel to their math problem? Because they needed to dry off those slippery calculations!
Now, onto your question. We can start by using Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force is the vector sum of the tension force and the friction force. Since the skier is pulled horizontally, the vertical forces (such as gravity) won't come into play here.
The tension force is given as 140 N, and we need to find the friction force. To do this, we need to find the acceleration of the skier first.
We can use the following kinematic equation: v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s since the skier starts from rest), a is the acceleration, and t is the time taken.
Plugging in the given values, we can solve for the acceleration:
6.0 m/s = 0 m/s + a(4.5 s)
Now, solve for a:
a = (6.0 m/s) / (4.5 s) = 1.33 m/s²
Now, we can use Newton's second law to find the friction force:
Force net = ma
(140 N) + F_friction = (75 kg)(1.33 m/s²)
Now, solve for F_friction:
F_friction = (75 kg)(1.33 m/s²) - 140 N
F_friction = 99.75 N - 140 N
F_friction ≈ -40.25 N
Wait a minute, that's negative! It means that the friction force is acting in the opposite direction of the motion.
So, to summarize, the magnitude of the friction force between the water skier's skis and the water is approximately 40.25 N. But remember, since it's negative, it is opposing the motion of the skier.
Sure! Let's break down the problem step by step.
Step 1: Identify the known values and the values you need to find.
Known values:
- Mass of the water skier (m) = 75 kg
- Initial velocity (v₀) = 0 m/s
- Final velocity (v) = 6.0 m/s
- Time taken (t) = 4.5 s
- Tension in the rope (F) = 140 N
Unknown value:
- Magnitude of the friction force between the skis and the water (F𝑓𝑟)
Step 2: Determine the acceleration of the skier.
Using the formula: v = v₀ + at
Substitute the known values:
6.0 = 0 + a(4.5)
Solve for acceleration (a).
Step 3: Use Newton's second law to find the net force acting on the skier.
Newton's second law states: F = ma.
Substitute the known values:
140 = 75(a)
Solve for the acceleration (a).
Step 4: Calculate the net force acting on the skier.
Using the formula: F = F𝑟 + F𝑓𝑟
Rearrange the formula:
F𝑟 = F - F𝑓𝑟
Substitute the known values:
F𝑟 = 140 - F𝑓𝑟
Step 5: Calculate the frictional force.
Substitute the value for F𝑟 into the rearranged formula.
Solve for F𝑓𝑟.
Step 6: Determine the magnitude of the frictional force.
Since frictional forces are always positive, take the absolute value of F𝑓𝑟 to find its magnitude.
That's it! Follow these steps, and you should be able to find the magnitude of the friction force between the skis and the water.
To find the magnitude of the friction force between the water skier's skis and the water, we need to first understand the forces acting on the skier.
In this scenario, there are three main forces at play: the tension force from the rope pulling the skier forward, the friction force opposing the skier's motion, and the gravitational force (weight) acting vertically downwards.
To determine the friction force, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Fnet = m * a
In this case, the net force is the difference between the tension force and the friction force:
Fnet = Ftension - Ffriction
Given:
- Mass of the skier, m = 75 kg
- Final velocity, vf = 6.0 m/s
- Time taken, t = 4.5 s
- Tension force, Ftension = 140 N
First, we need to calculate the acceleration of the skier using the formula:
vf = vi + a * t
Since the skier starts from rest, the initial velocity, vi, is 0 m/s. Rearranging the formula, we can solve for acceleration, a:
a = (vf - vi) / t
= (6.0 m/s - 0 m/s) / 4.5 s
= 6.0 m/s / 4.5 s
= 1.33 m/s²
Now that we know the acceleration, we can substitute the values into the net force equation:
Fnet = Ftension - Ffriction
m * a = Ftension - Ffriction
To find the friction force, we rearrange the equation:
Ffriction = Ftension - m * a
Plugging in the values, we get:
Ffriction = 140 N - (75 kg * 1.33 m/s²)
Calculating the product:
Ffriction = 140 N - 99.75 N
= 40.25 N
Therefore, the magnitude of the friction force between the skier's skis and the water is approximately 40.25 N.