A potential energy function for a certain system is given by U1(x) = Cx2 + Bx3. The potential energy function for a second system is given by U2(x) = A + Cx2 + Bx3, where A is a positive quantity. How does the force on system 1 relate to the force in system 2 at a given position?

A) The force in the two systems will be in opposite directions. B) The force is identical in the two systems. C) The force in the second system will be with less than the force in the first system. D) There is no relationship between the force in the two systems. E) The force in the second system will be with greater than the force in the first system. A) The force in the two systems will be in opposite directions. B) The force is identical in the two systems. C) The force in the second system will be with less than the force in the first system. D) There is no relationship between the force in the two systems. E) The force in the second system will be with greater than the force in the first system.

A moon of mass 4.00 × 1015 kg is in a circular orbit of radius 1.00 × 105 km about a planet of mass 6.00 × 1020 kg. Determine the potential energy of the system.

A) 1.60 × 1010 J B) 2.40 × 1031 J C) -1.60 × 1010 J D) -6.67 × 105 J E) -1.60 × 1018 J A) 1.60 × 1010 J B) 2.40 × 1031 J C) -1.60 × 1010 J D) -6.67 × 105 J E) -1.60 × 1018 J

A force acting on a 2.00 kg object is given by F(x) = (2.00 N/m)x + (1.00 N/m3)x3. An object starts at rest at x = 1.00 m. What is speed of the object when it reaches x = 2.00 m?

A) 1.23 m/s B) 0.650 m/s C) 2.60 m/s D) 1.78 m/s E) The object does not reach 2.00 m because the increase in potential energy would imply a negative kinetic energy. A) 1.23 m/s B) 0.650 m/s C) 2.60 m/s D) 1.78 m/s E) The object does not reach 2.00 m because the increase in potential energy would imply a negative kinetic energy.

Exam 8: Conservation of Energy

A 5.00-kg object moves clockwise around a 50.0 cm radius circular path. At one location, the speed of the object is 4.00 m/s. When the object next returns to this same location, the speed is 3.00 m/s. (a) How much work was done by non-conservative forces as the object moved once around the circle? (b) If the magnitude of the above non-conservative forces acting on the object is constant, what is the minimum value of this magnitude?

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Question 1

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(a) -17.5 J
(b) 5.57 N

A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position. (a) What is the maximum angle away from the lowest position the pendulum will reach? (b) What is the speed of the mass when the pendulum is 45° above its lowest position?

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Question 2

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(a) 50.5°
(b) 1.66 m/s

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope. When the skier reaches the bottom of the hill, her speed is 30.0 m/s. (a) How much work is done by friction as the skier comes down the hill? (b) What is the magnitude of the friction force if the skier travels directly down the hill?

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Question 3

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(a) -1.11 × 10⁴ J
(b) 55.3 N

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

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Question 4

A potential energy function for a certain system is given by U₁(x) = Cx² + Bx³. The potential energy function for a second system is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force in system 2 at a given position?

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Question 5

FIGURE 8-6 -An object was a mass of 10.0 kg is at rest at the top of a frictionless inclined plane of length 8.00 m and an angle of inclination 30.0° with the horizontal. The object is released from this position and it stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown in Fig. 8-6. The coefficient of kinetic friction for the horizontal surface of 0.400. (a) What is the kinetic energy of the object at the bottom of the inclined plane? (b) What is the speed of the object at the bottom of the inclined plane? (c) At what horizontal distance from the bottom of the inclined plane will this object stop?

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Question 6

Two identical balls are thrown from the top of a building with the same speed. Ball 1 is thrown horizontally, while ball 2 is thrown at an angle θ above the horizontal. Neglecting air resistance, which ball will have the greatest speed when hitting the ground below?

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Question 7

FIGURE 8-3 -Two inclined planes A and B have the same height but different angles of inclination with the horizontal. Inclided plane A has a steeper angle of inclination than inclined plane B. An object is released at rest from the top of each of the inclined planes. How does the speed of the object at the bottom of inclined plane A compare with that of the speed at the bottom of inclined plane B?

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Question 8

FIGURE 8-9 -6 J of work is needed to push an object of mass 2 kg from point A to point B of the frictionless inclined plane as shown in Fig. 8-9. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s².

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Question 9

The frictional force is a conservative force.

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Question 10

A mass of 3.0 kg is subject to a force F(x) = 8.0 N - (4.0 N/m)x. The potential energy of the mass is zero at x = 0. What is the potential energy of the mass at x = 2.0 m?

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Question 11

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 0.500 of its maximum height?

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Question 12

A moon of mass 4.00 × 10¹⁵ kg is in a circular orbit of radius 1.00 × 10⁵ km about a planet of mass 6.00 × 10²⁰ kg. Determine the potential energy of the system.

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Question 13

FIGURE 8-4 -A 2.0 g bead slides along a wire, as shown in Fig. 8-4. At point A, the bead is at rest. Neglect friction. (a) What is the potential energy of the bead at point A? (b) What is the kinetic energy of the bead at point B? (c) What is the speed of the bead at point B? (d) What is the speed of the bead at point C?

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Question 14

Neglecting air resistance, when you toss a stone straight up in the air from Earth's surface, which of the following statements is true for the upward motion of the stone.

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Question 15

How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare?

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Question 16

A force acting on a 2.00 kg object is given by F(x) = (2.00 N/m)x + (1.00 N/m³)x³. An object starts at rest at x = 1.00 m. What is speed of the object when it reaches x = 2.00 m?

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Question 17

Non-conservative forces can change the mechanical energy of a system.

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Question 18

The total mechanical energy of a system

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Question 19

A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential energy did the ball lose?

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Question 20

Showing 1 - 20 of 95

Exam 8: Conservation of Energy

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s2.

A potential energy function for a certain system is given by U1(x) = Cx2 + Bx3. The potential energy function for a second system is given by U2(x) = A + Cx2 + Bx3, where A is a positive quantity. How does the force on system 1 relate to the force in system 2 at a given position?

Two identical balls are thrown from the top of a building with the same speed. Ball 1 is thrown horizontally, while ball 2 is thrown at an angle θ above the horizontal. Neglecting air resistance, which ball will have the greatest speed when hitting the ground below?

FIGURE 8-9 -6 J of work is needed to push an object of mass 2 kg from point A to point B of the frictionless inclined plane as shown in Fig. 8-9. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s2.

The frictional force is a conservative force.

A mass of 3.0 kg is subject to a force F(x) = 8.0 N - (4.0 N/m)x. The potential energy of the mass is zero at x = 0. What is the potential energy of the mass at x = 2.0 m?

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 0.500 of its maximum height?

A moon of mass 4.00 × 1015 kg is in a circular orbit of radius 1.00 × 105 km about a planet of mass 6.00 × 1020 kg. Determine the potential energy of the system.

Neglecting air resistance, when you toss a stone straight up in the air from Earth's surface, which of the following statements is true for the upward motion of the stone.

How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare?

A force acting on a 2.00 kg object is given by F(x) = (2.00 N/m)x + (1.00 N/m3)x3. An object starts at rest at x = 1.00 m. What is speed of the object when it reaches x = 2.00 m?

Non-conservative forces can change the mechanical energy of a system.

The total mechanical energy of a system

A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential energy did the ball lose?

Introduction, Measurement, Estimating

Describing Motion: Kinematics in One Dimension

Kinematics in Two or Three Dimensions; Vectors

Dynamics: Newtons Laws of Motion

Using Newtons Laws: Friction, Circular Motion, Drag Forces

Gravitation and Newtons6 Synthesis

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Angular Momentum; General Rotation

Static Equilibrium; Elasticity and Fracture

Fluids

Oscillations

Wave Motion

Sound

Temperature, Thermal Expansion, and the Ideal Gas Law

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Second Law of Thermodynamics

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Gausss Law

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Electric Currents and Resistance

Dc Circuits

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Sources of Magnetic Field

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Inductance, Electromagnetic Oscillations, and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Light: Reflection and Refraction

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The Wave Nature of Light; Interference

Diffraction and Polarization

Special Theory of Relativity

Early Quantum Theory and Models of the Atom

Quantum Mechanics

Quantum Mechanics of Atoms

Molecules and Solids

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Nuclear Energy: Efects and Uses of Radiation

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A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

A potential energy function for a certain system is given by U₁(x) = Cx² + Bx³. The potential energy function for a second system is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force in system 2 at a given position?

FIGURE 8-9 -6 J of work is needed to push an object of mass 2 kg from point A to point B of the frictionless inclined plane as shown in Fig. 8-9. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s².

A moon of mass 4.00 × 10¹⁵ kg is in a circular orbit of radius 1.00 × 10⁵ km about a planet of mass 6.00 × 10²⁰ kg. Determine the potential energy of the system.

A force acting on a 2.00 kg object is given by F(x) = (2.00 N/m)x + (1.00 N/m³)x³. An object starts at rest at x = 1.00 m. What is speed of the object when it reaches x = 2.00 m?