Physics Chapter 9

A 1 kg ball is hung at the end of a rod 1 m long. If the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the rod?

1 kg

A rubber band is stretched by 1 cm when a force of 0.35 N is applied to each end. If instead a force of 0.70 N is applied to each end, estimate how far the rubber band will stretch from its unstretched length

2cm

A box is placed on a ramp in the configurations shown below. Friction prevents it from sliding. The center of mass of the box is indicated by a blue dot in each case. In which case(s) does the box tip over?

3 only

A (static) mobile hangs as shown below. The rods are massless and have lengths as indicated. The mass of the ball at the bottom right is 1 kg. What is the total mass of the mobile?

6 kg

A 60kg woman stands on the very end of a uniform board of length which is supported one quarter of the way from one end and is balanced. What is the mass of the board?

60kg

Can the sum of the torque on an object be zero while the net force on the object is nonzero?

Absolutely. Torques change the angular momentum of the object

Name the type of equilibrium for each position of the ball.

At A the ball is in unstable equilibrium, at B it is in stable equilibrium, and at C it is in neutral equilibrium.

Explain why touching your toes while you are seated on the floor with outstretched legs produces less stress on the lower spinal column than when touching your toes from a standing position.

Because when standing up and bending over to touch your toes gravity is pushing down directly upon your lower spinal column, and less stress is placed upon your lower spinal column when you are at the lowest possible point on the floor.

A parking garage is designed for two levels of cars. To make more money, the owner decides to double the size of the garage in each dimension (length, width, and number of levels). For the support columns to hold up four floors instead of two, how should he change the columns' diameter?

Double the area of the columns by increasing their diameter by a factor of square root of 2

A heavy ball suspended by a cable is pulled to the side by a horizontal force F. If angle theta is small, the magnitude of the force F can be less than the weight of the ball because:

F is equal to only the x component of the tension in the cable

You can find the center of gravity of a meter stick by resting it horizontally on your two index fingers, and then slowly drawing your fingers together. First the meter stick will slip on one finger, and then on the other, but eventually the fingers meet at the CG. Why does this work?

If the fingers are not the same distance from the CG, the finger closer to the CG will support a larger fraction of the weight of the meter stick so that the net torque on the stick is zero.

Why is it no possible to sit upright in a chair and rise to your feet without first leaning forward?

Its because your center of gravity is not aligned with your base of support. If you sit upright in a chair your feet(base of support) is not in line with your stomach(center of gravity) therefore in order for you to stand, you must first lean forward so that they will be perpendicular with each other..

A bungee jumper momentarily comes to rest at the bottom of the dive before he springs back upward. At the moment, is the bungee jumper in equilibrium?

No, because there is a net force acting on him.

A uniform meter stick supported at the 25 cm mark is in equilibrium when a 1 kg rock is suspended at the 0 cm end (as shown in the figure). Is the mass of the meter stick greater than, equal to, or less than the mass of the rock? Explain your reasoning.

The mass of the meter stick is 1 kg. The system is in equilibrium, so the torques must be balanced.

A 10N weight is suspended by two cords as shown. What can you say about the tension in the two cords?

The tension in the shorter cord is greater than the tension in the longer cord

Your doctor's scale has arms on which weights slide to counter your weight. These weights are much lighter than you are. How does this work?

This is because the docs scale is cleverly arranged so that the weight arms are essentially long levers, with the weights at the end of the levers.

Place yourself facing the edge of an open door. Position your feet astride the door with your nose and abdomen touching the door's edge. Try to rise on your tiptoes. Why can't this be done?

When you rise on your tiptoes your center of mass shifts forwards. But with your nose and abdomen against the door your CM can't shift forward and gravity exerts a torque on you which returns your feet to the floor.

Why is it more difficult to do sit-ups when your knees are bent than when your legs are stretched out?

When your legs are extended straight, the muscles on the top and side of your thighs, the hip flexors, do the work of lifting the torso. It is possible to lift your torso without using your abdominal muscles at all - and of course, it is easier

Examine how a pair of scissors or shears cut through a piece of cardboard. Is the name "shears" justified?

Yes the name "shears" is justified because when an object is under shear, it will have equal and opposite forces applied across it.

A ground retaining wall is shown in part (a) of the figure. The ground, particularly when wet, can exert a significant force F on the wall. (a) What force produces the torque to keep the wall upright? (b) Explain why the retaining wall in part (b) of the figure would be much less likely to overturn than that in part (a).

a) The weight of the wall exerts the torque to keep it upright. (b) The lever arm for the wall in (a) is small (half the width of the wall) so the torque due to its weight is small. For the wall in (b), in addition to the weight of the wall there is a torque due to the weight of horizontal part of the wall and the soil above it. This is a much larger force and has a much larger lever arm so the horizontal force exerted by the ground on the vertical part of the wall would have to be many tines larger in order to overturn it

Explain how to lay the cone on a flat table so that it is in (a) stable equilibrium, (b) unstable equilibrium, (c) neutral equilibrium.

a) resting on the open part ( /\ )is the most stable but that is stable only over a limited range, as tipping it too far will result in it falling into state (c) b) balanced in the tip ( \/ ) c) lying on it's side.

When you apply the torque equation sumT=0 to an object in equilibrium, the axis about which torques are calculated

can be located

Consider the two configurations of books shown below. Which of the following is true?

case 1 will tip

Which configuration of bricks is more likely to be stable?

figure B

A woman is balancing on a high wire which is tightly strung. The tension in the wire is...

much more than the woman's weight

A uniform beam is hinged at one end and held in a horizontal position by a cable. The tension in the cable..

must be at least half the weight of the beam, no matter what the angle of the cable.

Two children are balanced on opposite sides of a seesaw. If one child leans inward toward the pivot point, her side will

rise

Is Young's modulus for a bungee cord smaller or larger than that for an ordinary rope?

smaller

As you increase the force that you apply while pulling on a rope, which of the following is NOT affected?

the Young's modulus of the rope

Why do you tend to lean backwards when carrying a heavy load in your arms?

to keep your CG over your feet

A ladder, leaning against a wall,makes a 60 degrees angle with the ground. when is it more likely to slip: when a person stands near the top or near the bottom? explain.

top

Describe several situations in which an object is not in equilibrium, even though the net force on it is zero.

transitional and rotational equilibrium