Physics 3/4 Questions
Educational · TutoringQuestions
- A 2500 kg crate is pulled 8.2 m across a warehouse floor at a constant speed by a force of 1200 N. If the coefficient of kinetic friction between the crate and the floor is 0.48, calculate the energy transferred as heat due to friction.
2. A magnetic field with a strength of 4 T passes through a rectangular coil with an area of 3 m². If the magnetic field is perpendicular to the coil, what is the magnetic flux through the coil?
3. A bar magnet is moved through a coil of wire as shown below. The coil has a fixed orientation in space. Which of the following scenarios would produce the same magnitude of induced emf between the ends of the coil?
Scenario 1: A north pole enters the coil from the left.
Scenario 2: A south pole leaves the coil from the right.
Scenario 3: A north pole leaves the coil from the right.
Scenario 4: A south pole enters the coil from the left.
4. A satellite is orbiting a celestial body in a circular path with a period of $2 \times 10^4$ s and an orbital radius of $4 \times 10^6$ m. What is the approximate speed of the satellite in its orbit?
5. A planet orbits its star in an elliptical path. What type of force is responsible for keeping the planet in its orbit, preventing it from flying off into space?
A) Centrifugal force B) Gravitational force C) Frictional force D) Both centrifugal and gravitational forces acting together
6. A spacecraft is hovering at a distance of 3r from the center of a uniform spherical moon, where r is the moon's radius. If the gravitational field strength at the moon's surface is G N kg–1, what is the gravitational field strength at the spacecraft's location?
Answers and Explanations
Answer 1:
9!\text{Energy transferred as heat} = (2500 \times 9.8 \times 0.48) \times 8.2 = 9804 , \text{J} !9
However, since the question asks for energy transferred due to friction, and the force applied must equal the force of friction for the speed to be constant: 9!\text{Energy transferred as heat} = 1200 \times 8.2 = 9840 , \text{J} !9
The energy transferred as heat is equal to the work done by the friction force, which is the product of the friction force and the distance over which it acts. Since the force applied equals the friction force, we can directly calculate the energy transferred using the given force and distance values.
Answer 2:
8!\Phi = 12 , \text{Wb}!8
Magnetic flux is calculated by multiplying the magnetic field strength by the area it passes through, when the field is perpendicular to the area.
Answer 3:
Scenarios 1 and 3, and Scenarios 2 and 4, would produce the same magnitude of induced emf.
According to Faraday’s law of induction, the magnitude of the induced emf depends on the rate of change of the magnetic flux through the coil. When a north pole enters the coil, the magnetic flux increases in one direction, and when a north pole leaves the coil, the magnetic flux decreases in the same direction, resulting in the same magnitude of induced emf. Similarly, when a south pole enters or leaves the coil, the magnetic flux changes in the opposite direction, resulting in the same magnitude of induced emf.
Answer 4:
9!v \approx 314 \text{m s}^{-1} !9
Using the formula for the period of a circular orbit, 8!T = \frac{2\pi r}{v}!8, we can rearrange to solve for 8!v!8, giving 8!v = \frac{2\pi r}{T}!8. Plugging in the values, we get
9!v = \frac{2\pi \times 4 \times 10^6}{2 \times 10^4} \approx 314 , \text{m s}^{-1}!9
Answer 5:
B) Gravitational force
The gravitational force 8! F = \frac{Gm_1m_2}{r^2} !8 between the planet and its star provides the centripetal force necessary to keep the planet in orbit.
Answer 6:
8!\frac{G}{9}!8
Using the inverse square law, the gravitational field strength decreases with the square of the distance from the center of the moon. Since the spacecraft is 3r from the center, and the surface is r from the center (or 1r), the ratio of the distances squared is 8!\left(\frac{3r}{r}\right)^2 = 9!8. Therefore, the gravitational field strength at the spacecraft’s location is 8!\frac{1}{9}!8 of the surface value.