Unit 8 Learning Activities

To tighten a bolt, you push with a force of 80N at the end of a wrench handle that is 0.25 m from the axis of a bolt. (a) What torque are you exerting? (b) If you move your hand inward to be only .10 m from the bolt, what is the force you need to exert to have the same torque? (c) do the answers depend on the direction of your push relative to the direction of the wrench handle?

(a) The torque you exert when the lever arm is 0.25 m, is equal to T = (0.25 m x 80 N) = 20 N (b) When the lever arm is reduced to 0.10 m, the same torque can be achieved by exerting a force F given by the equation: 20 N x 0.10 m = F Solving for F, we get F = 200 N (c) Yes. Max torque is when the force is applied perpendicularly to the handle.

A racing car on a flat circular track needs friction between the tires and the track to maintain its circular motion. How much more friction is required for twice the speed.

2^2 =4 Four times the friction. So, when the speed of the car doubles, the required force of friction must quadruple.

Why doesn't the Leaning Tower of Pisa topple over?

A vertical line through the center of gravity passes inside its support base.

Beginning from a rest position, a solid disk A, a solid ball B, and a hoop C race down an inclined plane. In what order will they finish?

B,A,C. A round object with greater rotational inertia (relative to its own mass), has more resistance to changing its rotational speed than a round object with less rotational inertia. Thus, the hoop with the greatest rotational inertia will be the slowest.

Why is it easier to carry the same amount of water in two buckets, one in each hand, than in a single bucket?

Because you can stand up straight with two buckets instead of leaning over to one side. The CB will be at the center of the support base provided by your feet.

Why does a car nose up when accelerating and nose down when breaking?

Friction by the road on the tires produces a torque about the car's CM. When the car accelerates forward, the friction force points forward and rotates the car upward. The opposite occurs for braking.

In this chapter, we learned that an object may not be in mechanical equilibrium even when Σ F = 0. Explain

If two opposite forces are applied on a wheel, the forces would cause it to rotate, not stay still. The net force is zero, but the wheel will still rotate.

An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels are used, will the speedometer reading be high or low?

Low because the car will cover more ground with every rotation because of the larger tires. In other words, increasing the size of tires (without changing rotational speed) causes the car to travel faster on the road. As a result, the speedometer underestimates the real speed of the car.

When the line of action of a force intersects the center of mass of an object, can that force produce a torque about the object's center of mass?

No, because there is zero lever arm about the CM. Zero lever arm means zero torque.

Can a force produce a torque when there is no lever arm?

No.

Friction is needed for a car rounding a curve. But, if the road is banked, friction may not be required at all. What, then, supplies the needed centripetal force? (Hint: Consider vector components of the normal force on the car.)

On a banked road, the normal force has a horizontal component as shown, and it can supply the centripetal force needed to round the curve.

If the world's population moved to the North Pole and the South pole, would the 24-hour day become longer, shorter, or stay the same?

Shorter. If the world's population moves to the poles, the mass of humans on Earth would become concentrated near its axis of rotation. As a result, the rotational inertia of Earth decreases. However, in order for the angular momentum to remain constant, the rotational velocity of Earth must increase (spin faster), which in turn slightly reduces the length of the day.

Which will roll down an incline faster - a can of water or a can of ice?

The can of water is faster because when water inside the can slides, it contributes to weight rather than rotational inertia to the can.

Where is the center of mass of Earth's atmosphere?

The center of the Earth.

Explain why a long pole is more beneficial to a tightrope walker if the pole droops.

The drooping pole lowers the center of gravity of the pole, which increases it stability.

Where is the center of mass of a soccer ball?

The geometric center of a soccer ball.

You sit at the middle of a large turntable at an amusement park as it is set spinning and then allowed to spin freely. When you crawl toward the edge of the turntable, does the rate of rotation increase, decrease, or remain unchanged?

The rate of rotation decreases, according to the principle of conservation of angular momentum.

Use the equation v=rw to explain why the end of a flyswatter moves much faster than your wrist when swatting a fly.

The wrist and the swatter are lined up and rotate with the same rotational speed ϖ with respect to a wrist joint. So, according to the equation the speed of the wrist is rϖ and the speed of the end of the flyswatter is Rϖ. Since R is obviously greater than r, the speed (Rϖ) of the end of the fly swatter is greater than the speed (rϖ) of your wrist

How do clockwise and counterclockwise torques compare when a system is balanced?

They have equal values. They must be the same if the system is balanced, mechanical equilibrium.

What does a torque tend to do to an object?

Torque tends to twist or change the state of rotation of the object.

When a bowling ball leaves your hand, it may not spin. But farther along the alley, it does spin. What produces the spin?

When a non-spinning bowling ball touches the surface of the alley, there is an immediate backward frictional force with the floor. The resulting non-zero torque rotates the ball and causes it to roll forward.

Does the rotational inertia of a particular object differ for different axes of rotation? Can one object have more than one rotational inertia?

Yes.

As a car speeds up when rounding a curve, does the centripetal force on the car also increase?

Yes. Increased speed at the same radial distance means greater centripetal force. Without the greater centripetal force, the car will skid.

How would a ramp help you distinguish between two identical-looking spheres of the same weight, one solid and the other hollow?

You could roll them down the ramp. The hollow one will be slower than the solid one. The hollow one has more rotational inertia.

An ice puck of mass m revolves on an icy surface at speed v at the end of a horizontal string of length L. The tension in the string is T. (a) Write the equation for centripetal force, and substitute the values of T and L appropriately. Then with a bit of elementary algebra, rearrange the equation so that it solves for mass. (b) Show that the mass of the puck is 5 kg when the length of the string is 2 m, string tension is 10 N, and the tangential speed of the puck is 2 m/s.

centripetal force = (mass)(velocity)^2/radius T=mv^2/L = m = LT/v^2 m = (2m x 10N)/2^2 = 20/4 = 5 kg

Inertia depends on mass; rotational inertia depends on mass and something else. What?

velocity