Q1. What is the angle of inclination at which the force of static friction equals the component of weight acting down the slope for a coefficient of static friction of 0.4?
Solution:
The angle θ can be found using tan(θ) = μs. Thus, θ = arctan(0.4) ≈ 21.8 degrees.
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Q2. In a frictionless environment, what is the acceleration of an object in free fall?
Solution:
In a frictionless environment, all objects in free fall accelerate at 9.81 m/s² due to gravity.
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Q3. If a car travels 100 meters in 5 seconds, what is its average speed?
Solution:
Average speed is calculated as total distance divided by total time: 100 m / 5 s = 20 m/s.
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Q4. If a 150 kg object is on a slope of 15 degrees, what is the normal force acting on it?
Solution:
The normal force N = mg * cos(θ) = 150 kg * 9.81 m/s² * cos(15°) ≈ 1430 N.
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Q5. What is the acceleration of an object in free fall near the Earth's surface?
Solution:
The acceleration due to gravity near the Earth's surface is approximately 9.81 m/s².
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Q6. An object is thrown horizontally from a height of 45 m. How long does it take to hit the ground? (g = 9.8 m/s²)
Solution:
Using the formula s = 0.5gt², we have 45 = 0.5 * 9.8 * t², solving gives t ≈ 3.03 s.
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Q7. A car travels 100 meters in 4 seconds. What is its average speed?
Solution:
Average speed = total distance / total time = 100 m / 4 s = 25 m/s.
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Q8. A projectile is launched at an angle of 30 degrees with an initial velocity of 20 m/s. What is the horizontal component of its velocity?
Solution:
The horizontal component is given by v_x = v * cos(θ) = 20 * cos(30°) = 20 * (√3/2) ≈ 17.32 m/s.
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Q9. A ball is thrown vertically upwards with a speed of 20 m/s. How high will it go before it starts to fall back down? (g = 10 m/s²)
Solution:
Using the formula v² = u² + 2as, where v = 0, u = 20 m/s, and a = -10 m/s², we get 0 = 20² + 2 * (-10) * s, solving gives s = 20 m.
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Q10. A car accelerates from rest at a rate of 2 m/s². How far does it travel in 5 seconds?
Solution:
Using the formula s = ut + 0.5at², where u = 0, a = 2 m/s², and t = 5 s, we get s = 0 + 0.5 * 2 * 5² = 25 m.
