/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 117 If the person steps onto a smoot... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 117

If the person steps onto a smooth rock surface that's inclined at an angle large enough that these shoes begin to slip, what will happen? (a) She will slide a short distance and stop; (b) she will accelerate down the surface; (c) she will slide down the surface at constant speed; (d) we can't tell what will happen without knowing her mass.

Short Answer

Expert verified
The person will accelerate down the surface.

Step by step solution

01

Understand the concept of motion on an inclined plane

When a person steps on a smooth inclined surface, their motion is determined by gravity and the available friction between their shoes and the surface. Here, we can assume that the shoes are not providing enough friction to hold the person in place, so they begin to slip.
02

Assess the potential outcomes

For option (a), she will slide a short distance and stop, it's unlikely because without sufficient friction, there is practically no force to stop her from sliding down. For option (b), she will accelerate down the surface, it's the most realistic scenario as gravity will continuously pull her downwards leading to accelerated motion. For option (c), she will slide down the surface at constant speed, it's not feasible because gravity will keep acting and unless there is enough friction or a stopping force which isn't the case here, her speed would not remain constant. For option (d), we can't tell what will happen without knowing her mass, essentially, the mass isn't a determining factor in this case because regardless of it, she would still slip if the surface is smooth and inclined.
03

Formulate the outcome

Based on the analysis of all options, the most likely outcome would be that she will accelerate down the surface.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Friction and Gravity
Whenever you're on an inclined plane, two main forces are at play: friction and gravity. Gravity is what makes an object, or a person in this case, want to slide down the surface. It pulls everything toward the earth.
But what about friction? Friction is the force that tries to hold things in place as they move or try to move over a surface. It's the reason why we don't slip on flat surfaces easily. On a smooth inclined plane, however, friction might not be strong enough to counteract gravity.
  • Friction tries to prevent slipping by opposing motion.
  • Gravity always acts downwards, trying to pull you down the slope.
  • If the friction is too low, like on a smooth rock, you may start sliding.
When friction can't keep you steady, gravity takes over. This means you're likely to accelerate down the slope because the friction isn't enough to balance out the pull of gravity.
Accelerated Motion
When a person or object starts moving down a slope, the speed isn't constant. This is called accelerated motion. What this means is that the object gets faster and faster as it goes. Why does this happen?
Gravity continuously pulls the object down the slope. Because friction is too weak to fully counter this pulling force, the speed will keep increasing.
  • Acceleration happens because there's an unbalanced force.
  • Gravity causes this as it pulls you downhill.
  • Lack of enough friction means the motion isn't constant.
With constant acceleration, you'll keep speeding up until a force stops you or you reach a flat surface. So in our scenario, the person sliding will not stop or move at a steady pace; instead, she will keep going faster unless something else intervenes.
Effects of Inclination Angle
The angle of the slope plays a huge role in how motion occurs on an inclined plane. Steeper angles mean that gravity has a greater effect on the movement.
This is because the component of gravitational force pulling you down the slope becomes larger as the angle increases.
  • A steeper angle lessens the effect of friction.
  • The steeper the slope, the more you'll accelerate.
  • An angle too low may allow friction to prevent slipping.
As the angle of inclination goes up, it becomes harder for friction to counteract the force of gravity, leading to faster motion down the slope.
That's why even a slight increase in angle on a smooth surface can turn a gentle slope into a slippery challenge!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Runway Design. A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is \(700 \mathrm{~kg}\), and the total resistance (air drag plus friction with the runway on each may be assumed constant and equal to \(2500 \mathrm{~N}\). The tension in the towrope between the transport plane and the first glider is not to exceed \(12,000 \mathrm{~N}\). (a) If a speed of \(40 \mathrm{~m} / \mathrm{s}\) is required for takeoff, what minimum length of runway is needed? (b) What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

A \(3.00 \mathrm{~kg}\) box that is several hundred meters above the earth's surface is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope and results in a tension in the rope of \(T(t)=(36.0 \mathrm{~N} / \mathrm{s}) t\) The box is at rest at \(t=0 .\) The only forces on the box are the tension in the rope and gravity. (a) What is the velocity of the box at (i) \(t=1.00 \mathrm{~s}\) and (ii) \(t=3.00 \mathrm{~s} ?\) (b) What is the maximum distance that the box descends below its initial position? (c) At what value of \(t\) does the box return to its initial position?

\(\mathrm{A} 50.0 \mathrm{~kg}\) stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane. (a) If the plane's speed at the lowest point of the circle is \(95.0 \mathrm{~m} / \mathrm{s},\) what is the minimum radius of the circle so that the acceleration at this point will not exceed \(4.00 g ?\) (b) What is the apparent weight of the pilot at the lowest point of the pullout?

Some sliding rocks approach the base of a hill with a speed of \(12 \mathrm{~m} / \mathrm{s} .\) The hill rises at \(36^{\circ}\) above the horizontal and has coefficients of kinetic friction and static friction of 0.45 and \(0.65,\) respectively, with these rocks. (a) Find the acceleration of the rocks as they slide up the hill. (b) Once a rock reaches its highest point, will it stay there or slide down the hill? If it stays, show why. If it slides, find its acceleration on the way down.

A racetrack curve has radius \(120.0 \mathrm{~m}\) and is banked at an angle of \(18.0^{\circ} .\) The coefficient of static friction between the tires and the roadway is \(0.300 .\) A race car with mass \(900 \mathrm{~kg}\) rounds the curve with the minimum speed needed to not slide down the banking. (a) As the car rounds the curve, what is the normal force exerted on it by the road? (b) What is the car's speed?
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Force

Read Explanation

Measurements

Read Explanation

Energy Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Scientific Method Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.