Conservation of energy Knowledge-Based Practice

Questions

1. 1.

   Two blocks of masses $m_1 = 3.0\text{ kg}$ and $m_2 = 1.0\text{ kg}$ are connected by a light, inextensible string passing over a frictionless, massless pulley. If the system is released from rest, what is the speed of the blocks after $m_1$ has descended a vertical distance of 1.6 m? (Take $g = 10\text{ m/s}^2$.)

   • A) 4.0 m/s
   • B) 4.6 m/s
   • C) 4.9 m/s
   • D) 5.7 m/s
2. 2.

   A spring-loaded toy uses an ideal horizontal spring to launch a dart of mass m from rest along a frictionless track. If compressing the spring by a distance $x$ imparts a launch speed $v$ to the dart, what is the launch speed when the spring is compressed by a distance $2x$?

   • A) $\sqrt{2}v$
   • B) $2v$
   • C) $4v$
   • D) $8v$
3. 3.

   A 0.50 kg stone is launched from the edge of a 15 m high cliff with an initial speed of 10 m/s at an angle of $35^\circ$ above the horizontal. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the speed of the stone just before it strikes the ground?

   • A) 10 m/s
   • B) 15 m/s
   • C) 17 m/s
   • D) 20 m/s
4. 4.

   A simple pendulum consists of a 0.50 kg bob suspended by a 2.5 m light, inextensible string. If the bob is released from rest when the string makes an angle of $60^\circ$ with the vertical, what is its speed as it passes through the lowest point of its swing? (Neglect air resistance and take $g = 10\text{ m/s}^2$.)

   • A) 3.5 m/s
   • B) 5.0 m/s
   • C) 7.1 m/s
   • D) 8.7 m/s
5. 5.

   A 0.60 kg ball is thrown vertically upward from the ground with an initial speed of 20 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, at what height above the ground is the ball's kinetic energy equal to its gravitational potential energy?

   • A) 5.0 m
   • B) 10 m
   • C) 15 m
   • D) 20 m
6. 6.

   A 4.0 kg block is released from rest at the top of a rough ramp at a vertical height of 5.0 m and reaches the bottom with a speed of 8.0 m/s. Taking $g = 10\text{ m/s}^2$, how much mechanical energy is converted into thermal energy by friction as the block slides down the ramp?

   • A) 56 J
   • B) 72 J
   • C) 128 J
   • D) 200 J
7. 7.

   A 400 kg roller coaster car passes over the crest of a hill at a height of 22 m with a speed of 6.0 m/s. Neglecting friction and air resistance, and taking $g = 10\text{ m/s}^2$, what is the speed of the car when it reaches a lower section of the track at a height of 14 m?

   • A) 10 m/s
   • B) 14 m/s
   • C) 16 m/s
   • D) 20 m/s
8. 8.

   A 2.0 kg block slides along a frictionless horizontal surface with a speed of 6.0 m/s and strikes an ideal horizontal spring with a spring constant of 800 N/m. Assuming no mechanical energy is lost to the surroundings, what is the maximum compression of the spring?

   • A) 0.09 m
   • B) 0.15 m
   • C) 0.30 m
   • D) 0.60 m
9. 9.

   A 0.50 kg object is dropped from rest from a height of 20 m above the ground. Neglecting air resistance and taking $g = 9.8\text{ m/s}^2$, what is the kinetic energy of the object just before it strikes the ground?

   • A) 49 J
   • B) 98 J
   • C) 196 J
   • D) 392 J

Answers and step-by-step solutions appear after you finish the test.