Conservation of Energy

Questions and Answers

What is the unit of measurement for potential energy?

Watts

Kilograms

Newtons

Joules (correct)

What is the formula to calculate the potential energy of a particle?

mg/h

m/g^2h

mgh^2

mgh (correct)

A car is travelling at a constant velocity of 5 ms^-1 on a horizontal road. What is the acceleration of the car?

0 ms^-2 (correct)

20 ms^-2

10 ms^-2

5 ms^-2

What is the relationship between kilowatts (kW) and watts (W)?

1 kW = 1000 W Signup and view all the answers

A force of 500 N is acting on an object. If the object moves 2 meters, how much work is done?

1000 J Signup and view all the answers

What is the purpose of choosing a zero level when calculating potential energy?

To define a reference point for the potential energy Signup and view all the answers

A van is travelling at 6 ms^-1. If the engine is working at 24 kW, what is the acceleration of the van?

0.04 ms^-2 Signup and view all the answers

What is the maximum speed of the van, given that its engine is working at 24 kW and the constant resistance to motion has a magnitude of 600 N?

18 ms^-1 Signup and view all the answers

What is the work done against gravity equal to when a particle is raised vertically?

its change in potential energy Signup and view all the answers

What force is typically acting against a particle being raised vertically?

gravitational force Signup and view all the answers

What is the equation that relates force, mass, and acceleration?

F = ma Signup and view all the answers

What is the work-energy principle useful for?

solving problems involving external forces Signup and view all the answers

What is the unit of force in the equation 24000 = 𝐹𝐹𝐹𝐹?

newton Signup and view all the answers

What is the expression for force in terms of velocity and acceleration?

F = ma Signup and view all the answers

What is the equation that relates force, velocity, and acceleration in the problem 𝐹𝐹 - 600 = 1250(𝑎𝑎)?

F - 600 = 1250a Signup and view all the answers

What is the physical quantity that is being changed when a particle is raised vertically?

potential energy Signup and view all the answers

A particle of mass 0.2 kg is moving horizontally with a speed of 5 m/s. It then moves up an inclined plane, reaching a maximum height of 1.2 meters before momentarily coming to rest. What is the approximate work done by the gravitational force on the particle during its ascent?

-1.176 J Signup and view all the answers

A car of mass 1200 kg accelerates uniformly from rest to a speed of 25 m/s in 10 seconds. What is the average power delivered by the car's engine during this acceleration?

75 kW Signup and view all the answers

A 50 kg object is lifted vertically upwards at a constant speed of 2 m/s. What is the power output of the force lifting the object?

500 W Signup and view all the answers

A particle of mass 1 kg is released from rest at a height of 10 meters above the ground. Assuming no air resistance, what is the particle's speed just before it hits the ground?

14 m/s Signup and view all the answers

A car of mass 1000 kg is traveling at a constant speed of 20 m/s. The car then accelerates uniformly to a speed of 30 m/s over a distance of 100 meters. What is the average power delivered by the car's engine during this acceleration?

50 kW Signup and view all the answers

A particle is projected vertically upwards with an initial speed of 20 m/s. Assuming no air resistance, what is the maximum height reached by the particle?

20.4 m Signup and view all the answers

A ball of mass 0.5 kg is thrown vertically upwards with an initial speed of 10 m/s. What is the kinetic energy of the ball when it reaches its highest point?

0 J Signup and view all the answers

A 10 kg box is pushed along a horizontal surface with a constant force of 50 N. If the box moves at a constant speed of 2 m/s, what is the power output of the pushing force?

100 W Signup and view all the answers

What is the value of acceleration, represented by 'a', based on the provided equation?

2.72 ms −2 Signup and view all the answers

Which of the following best describes the work-energy principle in the context of the given content?

Work done is equal to the change in kinetic energy. Signup and view all the answers

How is work done calculated when a particle is raised vertically against gravity?

By multiplying the mass, height, and gravity. Signup and view all the answers

What initial value is given to work done on the left-hand side of the equation?

4000 Signup and view all the answers

What mathematical operation is performed to isolate 'a' in the equation?

Division by $1250$ Signup and view all the answers

How does gravitational force affect the calculation of work done in the provided context?

It serves as a constant factor in all energy calculations. Signup and view all the answers

Given the values in the equation, which other variable could potentially affect the calculation of 'a'?

The mass of the particle being lifted. Signup and view all the answers

In terms of energy transfer, what does raising a particle vertically against gravity primarily convert?

Kinetic energy into potential energy. Signup and view all the answers

What is the value of `a` in the equation `𝐹𝐹 − 2600𝑔𝑔 sin 4 − (800 + 5𝑣𝑣 2 ) = 2600𝑎𝑎` after substituting `𝑣𝑣 = 18 (𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐)`?

0 Signup and view all the answers

What is the value of `𝐹𝐹` in the equation `𝐹𝐹 − 10400𝑔𝑔 sin 4 − 2420 = 0` ?

9530 N Signup and view all the answers

What is the correct formula for the work done, `𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑`, based on the information provided?

𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = (0.35)(2𝑔𝑔 cos 30)(12) Signup and view all the answers

Which of the following is a correct expression for the work-energy principle, as mentioned in the text?

∆𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑏𝑏𝑏𝑏 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Signup and view all the answers

Study Notes

Energy Conservation in Motion

Total energy remains constant when only gravitational forces act on a particle.
Types of energy include kinetic energy (K.E) and potential energy (P.E), with P.E often referred to as gravitational potential energy (G.P.E).
Power (P) produced by an engine relates to driving force (F) and speed (v) using the formula: ( P = F \cdot v ).
K.E is calculated using the formula: ( K.E = \frac{1}{2} mv^2 ), where m is mass and v is speed.

Key Formulas

Potential energy is given by: ( P.E = mgh ), where h is the height above a reference level.
Power is measured in watts (W), with 1 kW equal to 1000 W, important for vehicle calculations.

Example Applications

A particle with a mass of 0.5 kg experiences motion on a smooth incline of 30°, starting from rest and reaching a speed of 6 m/s.

Work-Energy Principle

Work done against gravity equals the change in potential energy when a particle is raised: ( W = mgh ).
Constant resistance in motion needs to be accounted for when calculating vehicle acceleration and forces.

Example Calculation

For a van with a mass of 1250 kg traveling at 6 m/s, with engine power at 24 kW and resistance at 600 N:
- Calculate acceleration (a): ( 24000 - 600 = 1250a ) leading to ( a = 2.72 , \text{m/s}^2 ).

Context of External Forces

External forces, such as friction, impact energy calculations; the work-energy principle can aid in solving related problems.
Always select a fixed zero level for potential energy calculations to ensure accuracy.

Practical Implications

Understanding the relationship between kinetic/potential energy and work done is crucial for motion dynamics, particularly in vehicles.
Real-world scenarios often require considering both resistive and applied forces to determine resultant motions accurately.

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Description

Quiz on the concept of conservation of energy, where total energy remains constant when no external forces act on a particle, and its relation to kinetic and potential energy.