PHYS 2300 BYT1 Physics: Mechanics
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Free PHYS 2300 BYT1 Physics: Mechanics Questions
An object starts at rest and accelerates from time t, traveling a distance d. How far does the object travel, again starting from rest, in twice the time?
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d/4
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d/2
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d
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2d
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4d
Explanation
Explanation:
For constant acceleration from rest, displacement is given by s = ½ a t².
If the time is doubled to 2t while starting from rest under the same acceleration a:
s' = ½ a (2t)² = ½ a 4t² = 4 × (½ a t²) = 4d.
Correct Answer:
4d
Why Other Options Are Wrong:
d/4
This would mean the displacement decreases with longer time, which contradicts the quadratic relationship with time.
d/2
Halving the distance when doubling the time ignores that displacement grows with the square of time, not directly with time.
d
Keeping the distance the same at twice the time would only occur if acceleration were reduced, which is not stated.
2d
Doubling the distance suggests a linear relationship between distance and time, but for constant acceleration from rest, the distance is proportional to t², giving a factor of four.
A car is traveling at a speed of 80 m/s while navigating a circular track with a radius of 160 m. What is the magnitude of the centripetal acceleration experienced by the car in terms of g's?
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1 g
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2 g
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3 g
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4 g
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5 g
Explanation
Explanation:
Centripetal acceleration is given by the formula:
a_c = v² / r
where v is the velocity and r is the radius of the circular path. Substituting the given values:
a_c = (80)² / 160 = 6400 / 160 = 40 m/s²
To express this in terms of g (where g ≈ 9.8 m/s²):
a_c / g = 40 / 9.8 ≈ 4.08 ≈ 4 g
Thus, the car experiences approximately 4 times the acceleration due to gravity.
Correct Answer:
4 g
Why Other Options Are Wrong:
1 g
This is incorrect because the calculated centripetal acceleration is much larger than the acceleration due to gravity.
2 g
This is incorrect because the calculation shows the acceleration is roughly double this value, not 2 g.
3 g
This is incorrect because 3 g underestimates the actual centripetal acceleration of 40 m/s².
5 g
This is incorrect because it overestimates the acceleration; the correct value is approximately 4 g.
What is torque?
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The angle through which an object rotates
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The product of force exerted on an object
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The change in velocity per unit of time
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The measure of the force that can cause an object to rotate about an axis
Explanation
Explanation:
Torque is defined as the measure of the force that can cause an object to rotate about an axis. It depends not only on the magnitude of the force applied but also on the distance from the axis of rotation at which the force is applied, often referred to as the moment arm. This concept is fundamental in physics and engineering, as it explains how forces lead to rotational motion rather than linear motion. Unlike simply applying a force, torque specifically results in rotational acceleration of an object according to Newton’s second law for rotation.
Correct Answer:
The measure of the force that can cause an object to rotate about an axis
Why Other Options Are Wrong:
The angle through which an object rotates
This option describes rotational displacement, not torque. Torque refers to the rotational effect of a force, whereas the angle of rotation measures how far an object has turned. Confusing these two conflates the cause of rotation with its outcome.
The product of force exerted on an object
While torque involves force, it is not merely the product of any force. Torque specifically involves the force multiplied by the perpendicular distance to the axis of rotation. Simply multiplying force without considering this distance does not define torque.
The change in velocity per unit of time
This describes acceleration, which is a linear concept, not rotational. Torque may cause angular acceleration, but the definition of torque itself is not acceleration. This option incorrectly equates linear acceleration with rotational force.
Carrying a pile of dirt out in a wheelbarrow would represent which class of lever?
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Class 1
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Class 2
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Class 3
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Class 4
Explanation
Explanation:
The correct answer is "Class 2." In a Class 2 lever, the load is positioned between the fulcrum and the effort. In the case of a wheelbarrow, the wheel acts as the fulcrum, the load (dirt) is in the middle, and the person lifting the handles applies the effort at the opposite end. This arrangement allows a smaller effort to lift a heavier load, which is characteristic of Class 2 levers.
Correct Answer:
Class 2
Why Other Options Are Wrong:
Class 1
In a Class 1 lever, the fulcrum is between the effort and the load, such as in a seesaw. This does not describe a wheelbarrow, where the load is between the fulcrum and effort.
Class 3
In a Class 3 lever, the effort is applied between the fulcrum and the load, as in a pair of tongs or a broom. This does not match the wheelbarrow setup, where effort is applied at the opposite end from the fulcrum.
Class 4
Class 4 levers are not a standard classification in basic mechanics; typical levers are categorized as Class 1, 2, or 3. Therefore, this option is incorrect.
Which of the following statements is true about an object's weight but NOT about its mass
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It may vary depending on the object's location
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It is a measure of the amount of matter in the object
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It would be the same on the moon as it is on Earth
Explanation
Explanation:
The correct answer is "It may vary depending on the object's location." Weight is the force exerted by gravity on an object and is dependent on the local gravitational field. Therefore, an object will weigh less on the Moon than on Earth because the Moon’s gravity is weaker. Mass, on the other hand, is the amount of matter in an object and remains constant regardless of location. This distinction makes the statement about weight correct and unique compared to mass.
Correct Answer:
It may vary depending on the object's location
Why Other Options Are Wrong:
It is a measure of the amount of matter in the object
This describes mass, not weight. Mass remains constant regardless of gravitational influence, so this statement is not uniquely true for weight.
It would be the same on the moon as it is on Earth
This is incorrect because weight depends on gravity. An object weighs less on the Moon than on Earth, so this statement does not correctly describe weight.
A projectile is launched at an angle of 30° above the horizontal. Which other angle will yield the same horizontal range?
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15°
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30°
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60°
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75°
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90°
Explanation
Explanation:
For a projectile launched with the same speed and neglecting air resistance, the horizontal range is proportional to sin(2θ).
Two launch angles θ₁ and θ₂ give the same range when their sums equal 90°, because sin(2θ₁) = sin(2θ₂) when 2θ₂ = 180° − 2θ₁.
If θ₁ = 30°, then θ₂ = 90° − 30° = 60°.
Correct Answer:
60°
Why Other Options Are Wrong:
15°
The complement of 15° is 75°, not 30°, so it does not produce the same range as 30°.
30°
This is simply the same angle as the original and does not provide a distinct second angle with the same range.
75°
The complement of 75° is 15°, not 30°, so it will not match the range of a 30° launch.
90°
A 90° launch is straight upward, giving zero horizontal range, which is entirely different from the range at 30°.
A ball is thrown horizontally from the top of a tall cliff. Three seconds later, the ball has fallen a vertical distance of
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45 m.
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30 m
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20 m
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depends on the initial horizontal speed of the ball
Explanation
Explanation:
When a ball is thrown horizontally, its vertical motion is independent of its horizontal motion. The vertical distance fallen under gravity can be calculated using the free-fall formula:
d = ½ g t²
Assuming g ≈ 10 m/s² for simplicity and t = 3 s:
d = ½ × 10 × (3)² = 5 × 9 = 45 m
The vertical distance depends only on the time and acceleration due to gravity, not on the initial horizontal speed.
Correct Answer:
45 m.
Why Other Options Are Wrong:
30 m.
This is incorrect because it underestimates the vertical distance fallen. The correct calculation yields 45 m.
20 m.
This is incorrect because it significantly underestimates the free-fall distance over 3 seconds.
depends on the initial horizontal speed of the ball
This is incorrect because horizontal speed does not affect the vertical distance fallen in projectile motion; vertical and horizontal motions are independent.
When a rock is dropped, it will accelerate downward at a rate of 9.8 m/s². If the same rock is thrown downward (instead of being dropped from rest), its acceleration will be ____ (Ignore air resistance effects).
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less than 9.8 m/s²
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9.8 m/s²
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more than 9.8 m/s²
Explanation
Explanation:
Acceleration due to gravity is constant near the Earth's surface and does not depend on the initial velocity of the object. Whether a rock is dropped from rest or thrown downward, its acceleration remains 9.8 m/s². Only the initial velocity changes, affecting the speed at a given moment, but not the acceleration.
Correct Answer:
9.8 m/s²
Why Other Options Are Wrong:
less than 9.8 m/s²
This is incorrect because gravitational acceleration is independent of how the rock is released. It remains constant at 9.8 m/s².
more than 9.8 m/s²
This is incorrect because throwing the rock downward does not increase the gravitational acceleration. Only forces other than gravity could change the acceleration, which are ignored here.
An object is dropped and freely falls to the ground with an acceleration of 1 g. If it is thrown upward (neglecting air-resistance) at an angle instead, what will its acceleration be?
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0 g
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1 g downward
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1 g upward
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larger than 1 g
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none of these
Explanation
Explanation:
Acceleration due to gravity is constant near the Earth's surface and always acts downward, regardless of the motion of the object. Throwing an object upward at an angle does not change the gravitational acceleration acting on it; only its velocity components differ from a free fall. Therefore, the acceleration remains 1 g downward.
Correct Answer:
1 g downward
Why Other Options Are Wrong:
0 g.
This is incorrect because there is still a gravitational force acting on the object. The acceleration is not zero unless in free fall in a gravity-free environment.
1 g upward.
This is incorrect because gravity always acts downward, toward the center of the Earth, not upward.
larger than 1 g.
This is incorrect because gravitational acceleration is constant near the Earth's surface and does not increase due to the object's motion.
none of these
This is incorrect because the correct option is explicitly listed: 1 g downward.
A golf ball is thrown straight up at 10 m/s from the front seat of a convertible that is traveling at a constant velocity of 20 m/s forward. Where does the ball land when it comes back down? Ignore air resistance
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Behind the convertible
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In the front seat of the convertible
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To the side of the convertible
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In front of the convertible
Explanation
Explanation:
The golf ball initially has both the vertical velocity from the throw (10 m/s upward) and the horizontal velocity of the car (20 m/s forward). With no air resistance, there is no horizontal force, so the ball keeps the same horizontal speed as the car. Because the convertible continues at 20 m/s forward and the ball maintains 20 m/s forward horizontally, they stay aligned throughout the flight, so the ball comes down exactly where it was thrown relative to the car.
Correct Answer:
In the front seat of the convertible
Why Other Options Are Wrong:
Behind the convertible
Incorrect because the ball continues moving forward with the car’s initial horizontal velocity; it does not lag behind.
To the side of the convertible
Incorrect because no sideways force acts on the ball to move it left or right relative to the car.
In front of the convertible
Incorrect because the ball’s horizontal velocity matches the car’s, so it will not land ahead of the car.
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