Energy Work Power And Forces In Physics

1. A car of mass 1200 kg is travelling at 15 m/s. What is its kinetic energy?

9000 J

135000 J

18000 J

270000 J

Kinetic energy can be calculated using the formula KE = 0.5 * m * v², where m is the mass and v is the velocity. For a car with a mass of 1200 kg traveling at 15 m/s, the calculation is as follows: KE = 0.5 * 1200 kg * (15 m/s)² = 0.5 * 1200 * 225 = 135000 J. This shows that the kinetic energy of the car is 135000 joules, which represents the energy it possesses due to its motion.

Explanation

Kinetic energy can be calculated using the formula KE = 0.5 * m * v², where m is the mass and v is the velocity. For a car with a mass of 1200 kg traveling at 15 m/s, the calculation is as follows: KE = 0.5 * 1200 kg * (15 m/s)² = 0.5 * 1200 * 225 = 135000 J. This shows that the kinetic energy of the car is 135000 joules, which represents the energy it possesses due to its motion.

2. A rock of mass 5 kg is placed on a ledge 12 m above the ground. What is its gravitational potential energy? (g = 10 N/kg)

60 J

600 J

1200 J

120 J

Gravitational potential energy (GPE) is calculated using the formula GPE = mass × gravitational acceleration × height. Here, the mass of the rock is 5 kg, the gravitational acceleration is 10 N/kg, and the height is 12 m. Plugging in these values: GPE = 5 kg × 10 N/kg × 12 m = 600 J. Therefore, the gravitational potential energy of the rock on the ledge is 600 joules.

Explanation

Gravitational potential energy (GPE) is calculated using the formula GPE = mass × gravitational acceleration × height. Here, the mass of the rock is 5 kg, the gravitational acceleration is 10 N/kg, and the height is 12 m. Plugging in these values: GPE = 5 kg × 10 N/kg × 12 m = 600 J. Therefore, the gravitational potential energy of the rock on the ledge is 600 joules.

3. A person applies a force of 25 N to push a box across a floor. The box moves 6 m. How much work is done?

31 J

150 J

250 J

19 J

Work is calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the direction of motion. In this case, assuming the force is applied in the same direction as the box's movement (θ = 0°), the cosine factor is 1. Therefore, the work done is 25 N × 6 m = 150 J. This means that 150 joules of energy is transferred to the box as it is pushed across the floor.

Explanation

Work is calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the direction of motion. In this case, assuming the force is applied in the same direction as the box's movement (θ = 0°), the cosine factor is 1. Therefore, the work done is 25 N × 6 m = 150 J. This means that 150 joules of energy is transferred to the box as it is pushed across the floor.

4. A machine does 900 J of work in 15 seconds. What is its power output?

13500 W

915 W

60 W

45 W

Power is defined as the rate at which work is done, calculated using the formula \( \text{Power} = \frac{\text{Work}}{\text{Time}} \). In this case, the machine does 900 joules of work in 15 seconds. By substituting the values into the formula, we get \( \text{Power} = \frac{900 \, \text{J}}{15 \, \text{s}} = 60 \, \text{W} \). This indicates that the machine's power output is 60 watts, meaning it performs 60 joules of work each second.

Explanation

Power is defined as the rate at which work is done, calculated using the formula \( \text{Power} = \frac{\text{Work}}{\text{Time}} \). In this case, the machine does 900 joules of work in 15 seconds. By substituting the values into the formula, we get \( \text{Power} = \frac{900 \, \text{J}}{15 \, \text{s}} = 60 \, \text{W} \). This indicates that the machine's power output is 60 watts, meaning it performs 60 joules of work each second.

5. An object has a mass of 7 kg. What is its weight on Earth? (g = 10 N/kg)

7 N

17 N

70 N

700 N

Weight is calculated using the formula \( \text{Weight} = \text{mass} \times \text{gravity} \). For an object with a mass of 7 kg and gravitational acceleration of 10 N/kg on Earth, the weight would be \( 7 \, \text{kg} \times 10 \, \text{N/kg} = 70 \, \text{N} \). This means the object exerts a downward force of 70 Newtons due to Earth's gravity.

Explanation

Weight is calculated using the formula \( \text{Weight} = \text{mass} \times \text{gravity} \). For an object with a mass of 7 kg and gravitational acceleration of 10 N/kg on Earth, the weight would be \( 7 \, \text{kg} \times 10 \, \text{N/kg} = 70 \, \text{N} \). This means the object exerts a downward force of 70 Newtons due to Earth's gravity.

6. A ball is dropped from a height of 20 m. Just before it hits the ground, which statement best describes its energy?

All energy is gravitational potential energy

All energy has been converted to kinetic energy

Energy has been created from the fall

Kinetic energy and potential energy are both zero

As the ball falls from a height of 20 m, its gravitational potential energy decreases while its kinetic energy increases. Just before impact, all the potential energy has been converted into kinetic energy, assuming no energy losses due to air resistance. This conversion illustrates the principle of conservation of energy, where energy is transformed from one form to another without being lost. Thus, at the moment just before hitting the ground, the ball possesses maximum kinetic energy and minimal to zero potential energy.

Explanation

As the ball falls from a height of 20 m, its gravitational potential energy decreases while its kinetic energy increases. Just before impact, all the potential energy has been converted into kinetic energy, assuming no energy losses due to air resistance. This conversion illustrates the principle of conservation of energy, where energy is transformed from one form to another without being lost. Thus, at the moment just before hitting the ground, the ball possesses maximum kinetic energy and minimal to zero potential energy.

7. Two students lift identical boxes to the same height. Student A takes 8 seconds and Student B takes 20 seconds. Which of the following statements is correct?

Student B is more powerful because they took longer

Both students have the same power because they did the same work

Student A is more powerful because they completed the work in less time

Student A did more work because they were faster

Power is defined as the rate at which work is done. Although both students lifted the same weight to the same height, Student A completed the task in a shorter time (8 seconds) compared to Student B (20 seconds). Since power is calculated by dividing the work done by the time taken, Student A, who performed the work more quickly, has a higher power output. Therefore, the statement that Student A is more powerful is correct, as they did the same amount of work in less time, resulting in greater power.

Explanation

Power is defined as the rate at which work is done. Although both students lifted the same weight to the same height, Student A completed the task in a shorter time (8 seconds) compared to Student B (20 seconds). Since power is calculated by dividing the work done by the time taken, Student A, who performed the work more quickly, has a higher power output. Therefore, the statement that Student A is more powerful is correct, as they did the same amount of work in less time, resulting in greater power.