Answer:
4. The mass of 5 pebbles = 5 x 0.05 kg = 0.25 kg
Kinetic energy = 1/2 x mass x velocity^2
Kinetic energy = 1/2 x 0.25 kg x (25 m/s)^2 = 78.125 J
Estimate: Around 80 J
5. Mass of sports car = 1200 kg
Speed of sports car = 80 mph = 35.76 m/s (approx.)
Kinetic energy = 1/2 x mass x velocity^2
Kinetic energy = 1/2 x 1200 kg x (35.76 m/s)^2 = 906720 J
Estimate: Around 900,000 J
6. Mass of rock = 22 kg
Speed of rock = 9.0 m/s
Kinetic energy = 1/2 x mass x velocity^2
Kinetic energy = 1/2 x 22 kg x (9.0 m/s)^2 = 891 J
Estimate: Around 900 J
7. C. 200J
When the mass of an object doubles, its kinetic energy also doubles.
8. D. 400 J
When the velocity of an object doubles, its kinetic energy increases by a factor of four.
9. The kinetic energy of an object is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. Comparing the two balls, we can see that the first ball has a kinetic energy of 1/2 x 1.0 kg x (10 m/s)^2 = 50 J. The second ball has a kinetic energy of 1/2 x 10 kg x (1.0 m/s)^2 = 5 J. Therefore, the 1.0 kg ball moving at 10 m/s has more kinetic energy.
10. Kinetic energy = 1/2 x mass x velocity^2
100 J = 1/2 x 2.0 kg x velocity^2
velocity^2 = 100 J / (1.0 kg x 2.0) = 50
velocity = √50 m/s
Estimate: Around 7 m/s
11. Kinetic energy = 1/2 x mass x velocity^2
125000 J = 1/2 x 400 kg x velocity^2
velocity^2 = 125000 J / (200 kg) = 625
velocity = √625 m/s
Speed of motorcycle = 25 m/s
Estimate: Around 25 m/s
12. The kinetic energy of the horse and rider is given by KE = 1/2 mv^2, where m is the mass and v is the velocity. Since the kinetic energy should remain the same, we have KE = 1/2 m1v1^2 = 1/2 m2v2^2, where m1 is the mass of the horse and rider, m2 is the mass of the horse and a 100 kg rider, v1 is the initial speed, and v2 is the final speed we need to find.
Solving for v2:
v2 = sqrt((m1/m2)*v1^2) = sqrt((350+50)/100 * 19^2) = 25.85 m/s
Estimate: Around 25 m/s