Physics Chapter 6

Why are the main supporting cables of suspension bridges designed to sag the way they do?

By sagging, the horizontal component and the vertical component of the resultant vector formed between one end of the cable and the center of the cable is the lowest.

Why is speed classified as a scalar, and velocity as a vector?

Speed only represents the rate at which something is moving relative to another reference point. Velocity includes speed as well as the direction that object is moving.

What is the magnitude of the resultant of two vectors of magnitudes 4 and 3 that are at right angles to each other?

5.

How does a vector differ from a scalar?

A vector shows both magnitude and direction, while a scalar is a directionless quantity.

Why is less force required to push a barrel up a sloping ramp than to lift it vertically?

When you lift the barrel, your hands must do all the effort pushing against gravity. When you roll the barrel, the ground is able to alleviate some of the force that gravity is pushing downwards.

If a vector that is 1 cm long represents a force of 5 N, how many newtons does a vector 2 cm long, drawn to the same scale, represent?

10 N.

What is the magnitude of the resultant of a pair of 100-N vectors that are at right angles to each other?

100 rt 2.

Neglecting air resistance, if you throw a ball straight upward with a speed of 20 m/s, how fast will it be moving when you catch it?

20 m/s.

What is the resultant velocity of an airplane that normally flies at 200 km/h if it experiences a 50-km/h tailwind? A 50-km/h headwind?

250 km/h, 150 km/h.

At what angle should a slingshot be oriented for maximum altitude? For maximum horizontal range?

90°, 45°.

What is a parallelogram?

A parallelogram is a geometric shape that has 2 sets of parallel lines that are equal in length.

a. Neglecting air resistance, if you throw a baseball at 20 m/s to your friend who is on first base, will the catching speed be greater than, equal to, or less than 20 m/s? b. How about if air resistance is a factor?

Equal to, less than.

Distinguish between the method of geometric addition of vectors and vector resolution.

Geometric addition of vectors involves drawing one vector, then drawing the tail of the second vector on the head of the first vector and creating a resultant vector from the tail of the first vector to the head of the second vector. Vector resolution involves having a vector, and drawing the horizontal and vertical components of that vector.

Why does a ball rolling down an incline undergo more acceleration the steeper the incline?

The ball exerts less force from gravity at a steeper angle, which means that the ground pushes less on the ball at a steeper angle.

Why do electric power lines sometimes break in winter when a small weight of ice forms on them?

The horizontal component of the vector created when the strings are oriented directly due to the ice creates a lot of strain on the lines, breaking them.

In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant, and why does the vertical component change?

The horizontal component of velocity has no net force acting on it, so the velocity will not change. The vertical component changes because the earth is pulling the projectile towards itself, changing its velocity.

When a parallelogram is constructed in order to add forces, what represents the resultant of the forces?

The resultant is the diagonal of the parallelogram, with a corner at where the original vectors meet.

Why does a bowling ball move without acceleration when it rolls along a bowling alley?

There is no force that is accelerating it horizontally, and gravity can not accelerate it vertically because it is on the ground.

What is the net force, or equivalently, the resultant force that acts on an object when it is in equilibrium.

There is no net force.

What are the magnitudes of the horizontal and vertical components of a vector that is 100 units long, and oriented at 45°?

They are both (100/rt2) units long.

How does the downward component of the motion of a projectile compare to the motion of free fall?

They are the same.

At the instant a ball is thrown horizontally over a level range, a ball is held at the side of the first is released and drops to the ground. If air resistance can be neglected, which ball—the one thrown or the one dropped from rest— strikes the ground first?

They strike the ground at the same time.

The tension in a clothesline carrying a load of wash is appreciably greater when the clothesline is strung horizontally than when it is strung vertically. Why?

When the clothesline is vertical, there is only one vertical force that pulls the clothesline down, so the opposite force representing the tension on the string is low. When the clothesline is horizontal, the load of wash pulls the strings of the clothesline at an angle. Therefore, in order for the vertical component of the clothesline to match the vertical force exerted by the load, there must a horizontal vector that sums with the vertical vector to create the diagonal vector. This horizontal vector adds a great amount of stress to the string.

Compared to your weight, what is the stretching force in your arm when you let yourself hang motionless by one arm? By both arms vertically? Is this force greater or less if you hang with your hands wide apart? Why?

When you hang by one arm, your body pulls on the bar, so the bar pushes on your body through your arm. When you hang with both arms, the bar can push on your body through your arm, halving the strain in each arm. This force is greater if you hang with your hands apart because there is added strain of a horizontal force from your arms pulling the bar inwards: the bar pushes your arms outward as well as upwards, causing additional strain.

A boat is rowed at 8 km/h directly across a river that flows at 6 km/h. a. What is the resultant speed of the boat? b. How fast and in what direction can the boat be rowed to reach a destination directly across the river?

a. 10 km/h. b. It should be rowed at 10 km/h at an angle of 60° relative to the ground to the left of it.

a. What is the resultant of a pair of forces, 100 N upward and 75 N downward? b. What is their resultant if they both act downward?

a. 25 N upward. b. 175 N downward.

The weight of a ball rolling down an inclined plane can be broken into two vector components: one acting parallel to the plane, and the other acting perpendicular to the plane. a. At what slope angle are these two components equal? b. At what slope angle is the component parallel to the plane equal to zero? c. At what slope angle is the component parallel to the plane equal to the weight?

a. 45° b. 180° c. 90°

a. How far below an initial straight-line path will a projectile fall in one second? b.Does your answer depend on the angle of launch or on the initial speed of the projectile? Defend your answer.

a. 5 m. b. It does not depend on either, because gravity will accelerate the projectile by the same amount regardless of flight path or flight speed.

a. What is the maximum possible resultant of a pair of vectors, one of magnitude 5 and the other of magnitude 4? b. What is the minimum possible resultant?

a. 9 b. 1

a. A projectile is fired straight upward at 100 m/s. How fast is it moving at the instant it reaches the top of its trajectory? b. What is the answer if the projectile is fired upward at 45° instead?

a. It is stationary. b. It is moving at (100/rt 2) m/s.