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
What are the effects of gravity on earth?​
Sliva [168]

Answer:

Without it, we could not survive on Earth. Earth orbits the sun due to the gravity of the sun, which maintains us at a convenient distance from it to enjoy the sun's warmth and light. It keeps the air we need to breathe and our atmosphere in place. Our planet is held together by gravity.

5 0
2 years ago
Read 2 more answers
A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge is half the final value. The ti
vichka [17]

To solve this problem we will apply the expression of charge per unit of time in a capacitor with a given resistance. Mathematically said expression is given as

q(t) = e^{-\frac{t}{(R*C)}}

Here,

q = Charge

t = Time

R = Resistance

C = Capacitance

When the charge reach its half value it has passed 10ms, then the equation is,

\frac{1}{2}*q_{final} = e^{-\frac{0.01}{(R*C)}}

Ln(\frac{1}{2}) = -\frac{0.01}{RC}

- RC = \frac{0.01}{Ln(1/2)}

RC = 0.014s

We know that RC is equal to the time constant, then

T = RC  = 0.014s = 14ms

Therefore the time constant for the process is about 14ms

5 0
3 years ago
Now, find the concentration of H+ ions to OH– ions listed in Table B of your Student Guide for a solution at a pH = 11. Then div
Hunter-Best [27]

Answer

1.0/5

4

IlaMends

Ambitious

2.1K answers

12.9M people helped

Explanation:

When pH of the solution is 11.

..(1)

At pH = 11, the concentration of ions is .

When the pH of the solution is 6.

..(2)

At pH = 6, the concentration of ions is .

On dividing (1) by (2).

The ratio of hydrogen ions in solution of pH equal to 11 to the solution of pH equal to 6 is .

Difference between the ions at both pH:

This means that Hydrogen ions in a solution at pH = 7 has ions fewer than in a solution at a pH = 6

8 0
3 years ago
Read 2 more answers
Each rarefraction on a longitudinal wave correspond to what point on a transverse wave?
morpeh [17]
Answer: In a longitudinal wave, the crest and trough of a transverse wave correspond respectively to the compression, and the rarefaction. A compression is when the particles in the medium through which the wave is traveling are closer together than in its natural state, that is, when their density is greatest.
4 0
3 years ago
A net force acting on an object will always cause a change in the object's _________.
Nataly [62]
 cause a change in the object's velocity
3 0
3 years ago
Other questions:
  • Learning Goal:
    7·1 answer
  • Which of the following forms of light can be observed with telescopes at sea level?Select all that apply.Select all that apply.X
    7·1 answer
  • would the density of a person be the same on the surface of the earth and on the surface of the moon?
    15·1 answer
  • Are the correct? PLEASE HELP ASAP
    10·2 answers
  • You attach a 1.70 kg block to a horizontal spring that is fixed at one end. You pull the block until the spring is stretched by
    8·1 answer
  • It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months an
    6·1 answer
  • A water pump with a power of 3.4 × 102 watts lifts water at the rate of 7.5 × 10-2 meters/second from a water tank. What is the
    8·1 answer
  • the amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. what is the value of the time constant
    11·1 answer
  • You have been hired as a technical consultant for an early-morning cartoon series for children to make sure that the science is
    10·1 answer
  • Using knowledge of states of matter,write a message about the importance of science in our society​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!