"If a skier coasts down a slope at an angle of 24 degrees below the horizontal, what is her acceleration if the force of friction is negligible?"
I must have done this question 15 times, and still can't get the right anwser. Can anyone help me?
say she has mass m
there is a gravitational force down on her = m g
that force has a component normal (perpendicular) to the snow)=mg cos 24
there is an equal and opposite force up from the snow = mg cos 24
because there is no acceleration into or out of the snow.
HOWEVER, that gravitational force has another component down the slope = m g sin 24
There is no equal and opposite force to resist that because she is free to accelerate down the slope.
so
F = m a = m g sin 24
so
a = g sin 24
g is about 9.8 m/s^2
and sin 24 is about .407
Thank you so much; once I drew my slope levels correctly, it was no problem. Thanks again!
Oh, skiing down slopes can be quite puzzling, can't it? Well, fear not, my friend! I'm here to help you with your physics predicament. Now, when the force of friction is negligible, we can assume that the only forces acting on the skier are gravity and the normal force.
To find the acceleration, we can use a bit of trigonometry. The component of gravity that is parallel to the slope is mg sin(θ), where θ is the angle of the slope. So, the skier's acceleration is equal to mg sin(θ) divided by the mass of the skier.
Now, all you need to do is plug in the angle of 24 degrees (which, coincidentally, is the same angle I make when trying to solve a difficult problem), multiply it by the mass of the skier, and divide it by the mass again. And voila! You'll have your answer.
Just remember, when you're in doubt, trust in the power of math and a little bit of humor. Good luck, and may all your slopes be friction-free!
Yes, I can help you with that! To find the acceleration of the skier, we need to resolve the gravitational force acting down the slope into its components.
The gravitational force can be split into two components: one parallel to the slope (mg*sinθ) and one perpendicular to the slope (mg*cosθ), where θ is the angle of the slope.
Since the force of friction is negligible, the only force acting parallel to the slope is the component of the gravitational force. This force is given by mg*sinθ, where m is the mass of the skier and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the acceleration of the skier down the slope is equal to the component of the gravitational force parallel to the slope, divided by the skier's mass. This can be represented as:
a = (mg*sinθ) / m
The mass cancels out, leaving us with:
a = g*sinθ
Plugging in the values, we find:
a = 9.8 m/s^2 * sin(24°) ≈ 4.12 m/s^2
Therefore, the approximate acceleration of the skier down the slope is 4.12 m/s^2.
Of course! I can help you understand how to solve this problem. To find the acceleration of the skier, we can analyze the forces acting on her.
Firstly, we need to determine the components of the gravitational force acting on the skier in the direction of the slope and perpendicular to it. The component of gravity acting parallel to the slope is given by mg sinθ, where m is the mass of the skier and g is the acceleration due to gravity. The component of gravity acting perpendicular to the slope is mg cosθ.
Since the force of friction is negligible, the only force acting on the skier that causes acceleration is the component of gravity acting parallel to the slope. Therefore, we can say that this component of gravity is equal to the product of the mass of the skier (m) and her acceleration (a):
mg sinθ = ma
Next, we need to solve for the acceleration (a). We can cancel out the mass (m) from both sides of the equation:
g sinθ = a
Now, substitute the values into the equation:
a = g sinθ
The acceleration (a) is equal to the acceleration due to gravity (g) multiplied by the sine of the angle (θ). Remember to make sure that the angle is in radians if necessary.
Plug in the values for the angle (24 degrees) and the acceleration due to gravity (approximately 9.8 m/s^2), and calculate the result:
a = 9.8 m/s^2 * sin(24 degrees)
Using a calculator or a math software, we find that the acceleration is approximately 4.154 m/s^2 (rounded to three decimal places).
So, the skier's acceleration as she coasts down the slope at an angle of 24 degrees below the horizontal is approximately 4.154 m/s^2.