A-level Physics (Advancing Physics)/Forces and Power

Forces
Forces are vectors. When solving problems involving forces, it is best to think of them as lots of people pulling ropes attached to an object. The forces are all pulling in different directions, with different magnitudes, but the effect is in only one direction, with only one magnitude. So, you have to add the forces up as vectors.

Forces cause things to happen. They cause an object to accelerate in the same direction as the force. In other words, forces cause objects to move in a direction closer to the direction they are pulling in. If the object is already moving, then they will not cause it to move in the direction of the force, as forces do not create velocities: they create accelerations.

If a force is acting on an object, it seems logical that the object will not accelerate as much as a result of the force if it has a lower mass. This gives rise to the equation:

$$F = ma\,$$,

where F = force applied (in Newtons, denoted N), m = mass (in kg) and a = acceleration (in ms−2). If we rearrange the equation, it makes more sense:

$$a = \frac{F}{m}$$

In other words, the acceleration in a given direction as the result of a force is equal to the force applied per. unit mass in that direction.

Work Done
You should already know how to calculate some types of energy, for example:

$$\mbox{Kinetic Energy } = \frac{mv^2}{2}$$

$$\mbox{Gravitational Potential Energy } = mgh\,$$

The amount of energy converted by a force is equal to the work done, which is equal (as you already know) to the force multiplied by the distance the object it is acting on moves:

$$\mbox{Work Done } = \Delta E = F\Delta s\,$$

When answering questions about work done, you may be given a force acting in a direction other than that of the displacement. In this case, you will have to find the displacement in the direction of the force, as shown in the section on Vectors.

Power
Power is the rate of change of energy. It is the amount of energy converted per. unit time, and is measured in Js−1:

$$P = \frac{\Delta E}{t}$$,

where E = energy (in J) and t = time (in s). Since ΔE = work done, power is the rate at which work is done. Since:

$$\Delta E = F\Delta s\,$$

$$\frac{\Delta E}{t} = F\frac{\Delta s}{t}$$

$$P = Fv\,$$,

where P = power (in Watts, denoted W), F = force and v = velocity.

Gravity
Gravity is something of a special case. The acceleration due to gravity is denoted g, and is equal to 9.81359ms−2. It is uniform over small distances from the Earth. The force due to gravity is equal to mg, since F = ma. Therefore:

$$a = \frac{F}{m} = \frac{mg}{m} = g$$

Therefore, when things are dropped, they all fall at the same acceleration, regardless of mass. Also, the acceleration due to gravity (in ms−2) is equal to the gravitational field strength (in Nkg−1).

Questions
1. I hit a ball of mass 5g with a cue on a billiards table with a force of 20N. If friction opposes me with a force of 14.2N, what is the resultant acceleration of the ball away from the cue?

2. A 10g ball rolls down a 1.2m high slope, and leaves it with a velocity of 4ms−1. How much work is done by friction?

3. An electric train is powered on a 30kV power supply, where the current is 100A. The train is travelling at 90 kmh−1. What is the net force exerted on it in a forwards direction?

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