Chapter 1: Vectors and Projectiles
An object thrown vertically upwards returns at the same speed as the initial speed and duration as long as air resistance is negligible. When air resistance is factored in, the return speed will be altered. These alterations may result from the resistance to return velocity, which may drag the object to lower speeds.
For average velocity, we cannot have zero velocity and nonzero average acceleration at the same time. However instantaneous velocity could have the two concepts at the same time. For example. A stone thrown upwards would have an acceleration equal to gravitational pull hence where aav = -g.
It is real to have zero acceleration and non-zero velocity at the same time. This is the case since acceleration is a derivative of velocity and derivatives of a constant are zero. For instance, an object moving at a constant velocity has zero acceleration.'
Two or three vectors of unequal magnitude add up to give the zero vectors. The conditions are such that they should all be in a similar direction, and the magnitude of two should be equal but greater to the magnitude of the third.
The train would seem to be traveling backward since the reference frame is on the train that one is riding. The relative direction of the other train is backward since it is at a lower speed than the other one.
Absolutely no. As long as there is an increase in distance from the target, there should be an increase in the angle of aim as a result of the gravitational pull of the entire arrow to the downside.
Chapter 2: Newton's Law and Motion
The child will remain at rest unless there is an external force on her. Since the wagon would accelerate from beneath the child, the child would fall relative to the wagon as a result of instantaneous velocity applied.
Be definition of Newton's second law of motion, the net force, in this case, should be equal to zero. This statement holds for as far as the vector sum of the forces is zero relative to the forces acting on the object.
(a) A force is required to le the golf ball bounce back to the upside. As a result of the change in direction, the acceleration will be felt; hence, there should also be a force. (b) the pavement should create the force to the ball.
In finding the total acceleration, only their weights should be divided by their mass. As a result, the heavier rock should have twice as much force of gravity than the lighter block hence; acceleration should be equal for both.
It is the truck bed that tends to exert a force as a result of static friction on the crate. This causes an acceleration of the crate.
The magnitude of its acceleration is less on the descent than on the accent since there two forces that are opposite but parallel to each other on either way. These include weight and friction, and on the way up, they add to lead to greater acceleration than to the downside.
Weighing myself on an inclined plane would lead to a reading such that the magnitude of the normal force between the plane and I be defined by W costh.
Chapter 3: Circular Motion; Gravitation
Nothing can lead to an outward force hence; water is not expelled to the outside. Water is separated since it moves at a tangent to the rotation, out of the holes.
In the case of a gentle curve, acceleration is smaller than that of an object moving in a circular motion at a sharp curve.
The orbit would be affected in that it could be faster or farther. The gravitational force would double hence an effect on velocity or distance.
Chapter 4: Work and Energy and Conservation of Mechanical Energy; Power
Force, in this case, is at right angles with the displacement of the object; hence, zero work is done.
No work is done on the wall in this case because the wall does not move. One is applying a force and expelling energy for zero work.
When the skier descends, kinetic energy is recorded where some of it is transformed into heat energy. The remaining kinetic energy on the skier becomes kinetic energy of the snow when he hits it, making the snow to move. Some are also transformed into heat energy responsible for the movement of the snow.
The faster arrow will penetrate twice as far as the slower arrow. More kinetic energy would mean more work done by the faster arrow.
No, it cannot. Energy is conserved hence, preventing it from happening. Only a height lower than where it was dropped is where it would bounce back.
At a zigzag movement, there is a smaller angle of inclination as compared to a vertical movement up the trail. Work, after calculation, would be little for the zigzag movement as it is a longer path and only requires less force. This case is true since Work = force x distance
Chapter 5: Linear Momentum
To change the direction of a rocket in a vacuum, pilots should expel the exhaust in direct but opposite action to the change they need. This is Newton's third law of motion. Momentum during a change in direction is conserved hence, an easier shift of the rocket.
Yes, it is possible since the impulse, in this case, are a function of the force of impact and that which changes momentum. Multiplying the two would mean that impulse from a smaller force over a long time could be larger and vice versa.
The impact caused by the heavy load should be applying a torque on the person holding the heavy load. Leaning backward is an act that creates a counterbalance of the torque created with the torque of the weight of the body in a counterclockwise direction.
Chapter 6: Rotation
The odometer would read a larger distance. In every revolution, 27 inches are recorded whereas it could have only made a distance equal to 24 inches, which is the diameter of its wheels.
a) In the case of constant velocity, one point on the wheel would be radial and not tangential.
b) In a uniformly increasing angular velocity, the same point would have both radial and tangential components. The radial component is dependent on time whereas the tangential component is independent of time as angular acceleration remains the same.
c) In a constant angular velocity, both radial and tangential components would be constants.
Yes, a small force can exert a greater torque, when there is a large lever arm since torque is a factor if the product of force and the lever arm.
a) Net torque is not dependent on the net force of a system hence; net torque cannot be zero because the net force is zero.
b) The net force is not dependent on net torque either hence; net force cannot be zero because the net torque is zero.
a) Find an inclined plane and place both spheres on it
b) Find a stick to hold the two before simultaneously releasing them down the plane
c) Repeat the procedure a few times and keep watch. As a result of less rotational inertia, the solid sphere will rotate first compared to the hollow sphere as a result of their mass differences.
Chapter 7: Static Equilibrium and Material Strength
The bungee jumper is at equilibrium as it sits in a chair since its motion does not experience either velocity or acceleration in any case. Before any change in direction, the person is not in motion hence the truth in the statement.
It is expected to slip at the top or near the top. The action of gravity pushes the subject down, and since it is transferred to the bottom, the force pushes one out of the center of gravity, which should increase as one goes higher up.
As soon as one tries to get to their tiptoes, the point of support and center of mass should shift, letting the first be over the latter. The center of mass would remain behind the toes hence, letting one fall backward as no part can move past the door.
For a cantilever, tension forces occur at the top of the structure as opposed to a beam. Stone and ordinary concrete would be poor choices for either supports of the structure as a result of their weak tension, and using them as choices, would mean a weak cantilever structure
Chapter 8: Fluids at Rest and Fluids in Motion
The can is filled with steam when the water boils. Upon cooling, the steam condenses back to water leaving a partial vacuum that lets atmospheric pressure crush the can because of the pressure difference.
No, they would not have similar recordings because of the difference in volumes of the balloons. There would be differences in the space above the balloons.
Salty water is denser than fresh water hence more mass per volume for salty water. Denser liquids let objects or bodies float better on them. On displacing a similar amount of salt water, there would be more upward buoyant forces as compared to freshwater hence, the reason I would float better on salty water than on fresh water.
Yes, children may get sucked under a rapidly moving train as a result of Bernoulli's principle. As a result of the air surrounding the train, the children may feel lower air pressure on them as compared to air pressure around the train. The pressure difference would create a force, which is large enough to let the child get sucked under the train.
At the wind, pilots should be able to see the wheels of the plane leave the land faster. The impact of a headwind of a certain speed would lead to a relatively lower take-off speed of the plane. Additionally, air pressure contributes to a plane's take-off in that wind traveling at the top of the plane's wing would create a suction effect on the upper surface hence, letting the plane take off easily as compared to a situation where wind passes beneath the surface.
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