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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.

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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!

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Most popular questions from this chapter

Jack sits in the chair of a Ferris wheel that is rotating at a constant \(0.100 \mathrm{rev} / \mathrm{s}\). As Jack passes through the highest point of his circular path, the upward force that the chair exerts on him is equal to one- fourth of his weight. What is the radius of the circle in which Jack travels? Treat him as a point mass.

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 box with mass \(m\) is dragged across a level floor with coefficient of kinetic friction \(\mu_{\mathrm{k}}\) by a rope that is pulled upward at an angle \(\theta\) above the horizontal with a force of magnitude \(F\). (a) In terms of \(m, \mu_{\mathrm{k}}, \theta,\) and \(g,\) obtain an expression for the magnitude of the force required to move the box with constant speed. (b) Knowing that you are studying physics, a CPR instructor asks you how much force it would take to slide a \(90 \mathrm{~kg}\) patient across a floor at constant speed by pulling on him at an angle of \(25^{\circ}\) above the horizontal. By dragging weights wrapped in an old pair of pants down the hall with a spring balance, you find that \(\mu_{\mathrm{k}}=0.35 .\) Use the result of part (a) to answer the instructor's question.

A box with mass \(m\) sits at the bottom of a long ramp that is sloped upward at an angle \(\alpha\) above the horizontal. You give the box a quick shove, and after it leaves your hands it is moving up the ramp with an initial speed \(v_{0}\). The box travels a distance \(d\) up the ramp and then slides back down. When it returns to its starting point, the speed of the box is half the speed it started with; it has speed \(v_{0} / 2 .\) What is the coefficient of kinetic friction between the box and the ramp? (Your answer should depend on only \(\alpha\).)

Forces During Chin-ups. When you do a chin-up, you raise your chin just over a bar (the chinning bar), supporting yourself with only your arms. Typically, the body below the arms is raised by about \(30 \mathrm{~cm}\) in a time of \(1.0 \mathrm{~s},\) starting from rest. Assume that the entire body of a \(680 \mathrm{~N}\) person doing chin-ups is raised by \(30 \mathrm{~cm},\) and that half the \(1.0 \mathrm{~s}\) is spent accelerating upward and the other half accelerating downward, uniformly in both cases. Draw a free-body diagram of the person's body, and use it to find the force his arms must exert on him during the accelerating part of the chin-up.
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