1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SIZIF [17.4K]
3 years ago
8

A girl is sledding down a slope that is inclined at 30º with respect to the horizontal. The wind is aiding the motion by providi

ng a steady force of 161 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 87.7 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.151. How much time is required for the sled to travel down a 271-m slope, starting from rest?

Physics
1 answer:
OleMash [197]3 years ago
8 0

Answer:

The sled required 9.96 s to travel down the slope.

Explanation:

Please, see the figure for a description of the problem. In red are the x and y-components of the gravity force (Fg). Since the y-component of Fg (Fgy) is of equal magnitude as Fn but in the opposite direction, both forces get canceled.

Then, the forces that cause the acceleration of the sled are the force of the wind (Fw), the friction force (Ff) and the x-component of the gravity force (Fgx).

The sum of all these forces make the sled move. Finding the resulting force will allow us to find the acceleration of the sled and, with it, we can find the time the sled travel.

The magnitude of the friction force is calculated as follows:

Ff = μ · Fn

where :

μ = coefficient of kinetic friction

Fn =  normal force

The normal force has the same magnitude as the y-component of the gravity force:

Fgy = Fg · cos 30º = m · g · cos 30º

Where

m = mass

g = acceleration due to gravity

Then:

Fgy = m · g · cos 30º = 87.7 kg · 9.8 m/s² · cos 30º

Fgy = 744 N

Then, the magnitude of Fn is also 744 N and the friction force will be:

Ff = μ · Fn = 0.151 · 744 N = 112 N

The x-component of Fg, Fgx, is calculated as follows:

Fgx = Fg · sin 30º = m·g · sin 30º = 87.7 kg · 9.8 m/s² · sin 30º = 430 N

The resulting force, Fr, will be the sum of all these forces:

Fw + Fgx - Ff = Fr

(Notice that forces are vectors and the direction of the friction force is opposite to the other forces, then, it has to be of opposite sign).

Fr = 161 N + 430 N - 112 N = 479 N

With this resulting force, we can calculate the acceleration of the sled:

F = m·a

where:

F = force

m = mass of the object

a = acceleration

Then:

F/m = a

a = 479N/87.7 kg = 5.46 m/s²

The equation for the position of an accelerated object moving in a straight line is as follows:

x = x0 + v0 · t + 1/2 · a · t²

where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

Since the sled starts from rest and the origin of the reference system is located where the sled starts sliding, x0 and v0 = 0.

x = 1/2· a ·t²

Let´s find the time at which the position of the sled is 271 m:

271 m = 1/2 · 5.46 m/s² · t²

2 · 271 m / 5.46 m/s² = t²

<u>t = 9.96 s </u>

The sled required almost 10 s to travel down the slope.

You might be interested in
I need help ASAPP
Tresset [83]

Answer: For the first part the answer is Radio Waves and the second part’s answer is gamma ray.

6 0
3 years ago
Wat's the definition of microwave spectroscopy
ivann1987 [24]

Answer:

Microwave spectroscopy is the spectroscopy method that employs microwaves, i.e. electromagnetic radiation at GHz frequencies, for the study of matter

6 0
3 years ago
Next weekend you are going to Eleanor Rigby’s house to fix her grandfather clock that is a bit slow. Based on what you have lear
Bumek [7]

Answer:

By pushing the pendulum Bob up so it moves faster

Explanation:

In pendulum physics the length of the pendulum Bob determines the speed of the clock. So since the grandfather's clock is slow it means the Bob is has moved down so to move it up you have to achieve this by adjusting the but upwards thereby making the clock move faster.

8 0
3 years ago
The launch speed of a projectile is three times the speed it has at its maximum height.what is the elevation angle at launch?
Sphinxa [80]

Answer:

Given: a projectile of initial launch velocity(V) and launch angle ∅ and no air resistance. At the maximum height, the projectile would have a zero contribution of speed from the vertical component(Vy) Therefore, if we say Vx=Vcos∅ is the only speed the projectile has at the instant of maximum height then we can replace Vx with 1/5V and write 1/5V=Vcos∅. Solving for the the launch angle ∅, gives Inverse Cos(1/5)=78.5 degrees.

6 0
2 years ago
The energy of motion best describes which of the following
Ivahew [28]
Energy of motion is the literal definition of kinetic energy
8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the momentum of a 5 kg object that has a velocity of 1.2 m/s?
    12·2 answers
  • Based on the law of conversation of energy how can we reasonably improve a machines ability to do work?
    5·1 answer
  • A piano has a mass of 185 kg, and the coefficient of friction between it and the floor is 0.39. What is the maximum force of fri
    8·2 answers
  • What would be the first thing you would do if your clothes caught fire while working in a laboratory? select one of the options
    12·1 answer
  • What is the difference between free fall and weightlessness
    9·2 answers
  • Where is the Ring Of Fire located?
    13·2 answers
  • If the speed of a ball increased from 1m/s to 4m/s by how much would kinetic energy increase
    5·1 answer
  • What is the mass of a stone moving at a speed of 15 meters/second and having a momentum of 7.5 kilogram - meters / seconds
    9·2 answers
  • If everything lines up perfectly for superposition to occur, these massive waves would break with a force of 100 metric tons per
    15·1 answer
  • A 77 kg student traveling in a car with a constant velocity has a kinetic energy of 1.7 104 J. What is the speedometer reading o
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!