What is the approximate mass of a pencil?
- A) 5.0 x 10-1 kg
- B) 5.0 x 10-3 kg
- C) 5.0 x 100 kg
- D) 5.0 x 101 kg
The diagram below shows a granite block being slid at constant speed across a horizontal concrete floor by a force parallel to the floor. Which pair of quantities could be used to determine the coefficient of friction for the granite on the concrete?
- A) mass and normal force on the block
- B) mass and speed of the block
- C) frictional force and speed of the block
- D) frictional force and normal force on block
A net force of 23 newtons is applied horizontally to a 10. kilogram block resting on a table. What is the magnitude of the acceleration of the block?
A 15-kilogram mass weighs 60. newtons on planet X. The mass is allowed to fall freely from rest near the surface of the planet. After falling for 6.0 seconds, what is the acceleration of the mass?
- A) 10. m/s2
- B) 24 m/s2
- C) 4.0 m/s2
- D) 0.25 m/s2
Which is a derived unit?
- A) kilogram
- B) meter
- C) newton
- D) second
The correct answer and explanation is:
Here are the correct answers to the questions:
- Approximate mass of a pencil:
Answer: B) 5.0 x 10⁻³ kg
A typical wooden pencil weighs around 5 grams, which is 5.0 × 10⁻³ kg in SI units. This makes option B the correct choice. The other choices are significantly too high for a standard pencil. - Quantities to determine the coefficient of friction:
Answer: D) Frictional force and normal force on block
The coefficient of friction (μ) is given by the formula: μ=FfFn\mu = \frac{F_f}{F_n} where FfF_f is the frictional force and FnF_n is the normal force. Since friction depends on the normal force and not on mass or speed alone, option D is the correct answer. - Magnitude of acceleration of a 10 kg block with a 23 N force applied:
Using Newton’s second law: F=maF = ma Given F=23NF = 23 N and m=10kgm = 10 kg, we solve for aa: a=Fm=2310=2.3 m/s2a = \frac{F}{m} = \frac{23}{10} = 2.3 \text{ m/s}^2 Thus, the acceleration is 2.3 m/s². - Acceleration of a 15-kg mass on planet X:
Using the formula for weight: W=mgW = mg Given that the weight W=60W = 60 N and mass m=15m = 15 kg, we solve for gg: g=Wm=6015=4.0 m/s2g = \frac{W}{m} = \frac{60}{15} = 4.0 \text{ m/s}^2 Thus, the acceleration due to gravity on planet X is 4.0 m/s², making the correct answer C) 4.0 m/s². - Derived unit:
Answer: C) Newton
A derived unit is one that is formed from the base SI units. The newton (N) is derived from the formula: N=kg⋅m/s2N = kg \cdot m/s^2 In contrast, kilogram (kg), meter (m), and second (s) are fundamental (base) SI units.
Explanation
Understanding units, forces, and motion is crucial in physics. The mass of a pencil is relatively small, around 5 grams (5.0 × 10⁻³ kg), making answer B correct. Heavier objects such as books or laptops would fall into much higher mass ranges.
To determine the coefficient of friction between two surfaces, we use the ratio of the frictional force to the normal force. Since normal force counteracts the gravitational force on a horizontal surface, measuring both these forces allows us to calculate friction, making option D correct.
Newton’s second law, F = ma, is fundamental in physics. It explains how force and mass determine acceleration. When a force of 23 N is applied to a 10 kg block, dividing the force by the mass gives an acceleration of 2.3 m/s².
Gravitational acceleration differs by location. On Earth, g = 9.8 m/s², but on planet X, where a 15 kg object weighs 60 N, using g = W/m gives 4.0 m/s² as the gravitational acceleration.
A derived unit is a combination of base SI units. The newton (N) is derived from mass (kg), length (m), and time (s), while kilogram, meter, and second are fundamental units.
Physics is a precise and logical science that relies on measurement and mathematical principles. Understanding these concepts helps in practical applications, from engineering to space exploration.
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