Physics, 04.07.2019 08:00 karen7088

Calculate the acceleration of a skier heading down a 10.0º slope, assuming the coefficient of friction for waxed wood on wet snow. (b) find the angle of the slope down which this skier could coast at a constant velocity. you can neglect air resistance in both parts, and you will find the result of exercise 5.9 to be useful. explicitly show how you follow the steps in the problem-solving strategies.

Answers: 1

Show answers

Answers

Acceleration of a skier heading down a 10.0º slope is 0.74 m/s² and the angle of the slope down which this skier could coast at a constant velocity is 5.7 degrees.

What is the acceleration of the object?

Acceleration of a object is the rate of change of velocity of the object per unit time.

Negative velocity of the object indicates the direction of object is backward, and positive velocity of the object indicates the direction of object is forward.

(a) The acceleration of a skier heading down a 10.0º slope-

From the second law of motion, the net force is equal to the mass times' acceleration. The net force on the body is due to own weight and friction force.

$W+F_f=ma\\mg\sin\theta+(-\mu mg\cos \theta)=ma\\a=g(\sin\theta-\mu \cos\theta)\\$ ........1

Put the values as,

$a=9.81[\sin(10)-0.1\times \cos (10)]\\a=0.74\rm m/s^2$

(b) The angle of the slope down which this skier could coast at a constant velocity-

For the constant velocity, the value of acceleration should be zero. Put the value of acceleration 0 in the equation 1 as,

$0=9.81(\sin\theta-0.1\times\cos\theta)\\\dfrac{\sin\theta}{\cos\theta}=0.1\\tan\theta=0.1\\\theta=5.7^o$

Acceleration of a skier heading down a 10.0º slope is 0.74 m/s² and the angle of the slope down which this skier could coast at a constant velocity is 5.7 degrees.

Learn more about the acceleration here;

link

Answer from: jessebeck0805

(a) 0.74 m/s^2

Explanation:

There are two forces acting on the skier: the component of the weight parallel to the slope, which acts downward, and the frictional force, which acts upward along the incline.

The component of the weight parallel to the inclined plane is:

$W= m g sin \theta$

where m is the mass of the skier, g=9.81 m/s^2 and $\theta=10^{\circ}$ .

The frictional force is instead

$F_f = -\mu m g cos \theta$

$\mu=0.1$ is the coefficient of friction for waxed wood on wet snow.

If we apply Newton's second law, we can write that the net force must be equal to the product of mass per acceleration:

$mgsin \theta -\mu mg cos \theta =ma$

And symplifying m, we can find the acceleration:

$a=g sin \theta-\mu g cos \theta=$

$=(9.81 m/s^2)(sin 10^{\circ})-(0.1)(9.81 m/s^2)(cos 10^{\circ})=0.74 m/s^2$

(b) $5.7^{\circ}$

Explanation:

This time, the skier is moving at constant velocity. Therefore, the acceleration is zero (a=0) and Newton's second law becomes:

$mg sin \theta - \mu m g cos \theta=0$

By simplifying, we get

$tan \theta = \mu$

From which we can find the angle at which the skier could coast at a constant velocity:

$\theta= tan^{-1} (\mu) = tan^{-1} (0.1)=5.7^{\circ}$

Answer from: Quest

did yall get answers for this yet

Answer from: Quest

Answer59.2kg; /

Another question on Physics

Physics, 21.06.2019 22:00

Why do electron microscopes have higher resolving power than light microscopes?

Answers: 1

Answer

Physics, 22.06.2019 05:30

James is trying to prove newton's 2nd law of motion. he tries to move four different objects with different masses, shapes, and sizes from point a to point b. the objects are a toy car, a car, a refrigerator, and a kitchen table. after some experimentation, he finds that force is dependent on the mass of the object, rather than it's size or shape. the object that takes the most force to move is the

Answers: 1

Answer

Physics, 22.06.2019 10:00

Need people build a dam to create a reservoir that supplies water a nearby city needs. describe two ways this action will likely affect the water cycle in the local environment. (5 points) worth 20 points

Answers: 1

Answer

Physics, 22.06.2019 19:30

Another word for electromagnetic energy is a. heat b. force c. matter d. radiation

Answers: 1

Answer

You know the right answer?

Calculate the acceleration of a skier heading down a 10.0º slope, assuming the coefficient of fricti...

Questions