The angle of Deviation and Speed of a Toy Car

Problem: How the angle of deviation affect the speed of a toy car.

Introduction

Speed can be defined as the distance travelled by an object over time. Distance is a measure of length covered by a moving object. Speed is a scalar quantity denoted in m/s. Other units can be km/hr, cm/s. An object is said to be in uniform speed if it covers the same length in an equal duration of time regardless of how little the intervals are. On the other hand, for non-uniform (variable) speed, the distances covered are unequal in equal durations. Lastly, the average speed is the ratio of length covered to the time taken.

Average speed =  = ……………………………..eqn 1

Factors that affect the speed of a moving object, in our case the toy, are weight, horizontal distance, time, friction and angle of deviation. The higher the mass, the lower the speed while holding other factors constant. The object’s weight affects speed down a ramp due to the pull of gravity. When the car leaves the ramp, friction and mass affect speed. The momentum increases with an increase in the toy car’s mass, which allows the car to move faster with the same amount of friction (Wick & Ramsdell, 2002). This experiment will primarily focus on the angle of deviation.  

The angle of deviation is defined as the degree of deviation of a body from the upright. The angle of elevation is the angle from the horizontal upward to an object. The line of sight of the observer would be above the horizontal. The following diagrams show the similarity between the angle of deviation and elevation angle.

Figure 1: Angle of deviation and angle of elevation

The energy caused by motion is called kinetic energy. It is the energy that the moving body posses. The higher the speed, the higher the energy possessed (Pendrill et al., 2014). Thus, if the angle of deviation influences speed, it influences the kinetic energy.

Aim

The experiment investigates how the variation of angle of deviation affects the toy car’s speed.

Hypothesis

The toy’s speed moving down a ramp will either increase or decrease if the angle of deviation is varied. The angle is varied by increasing the ramp height. Alternatively, the kinetic energy in the moving toy would either reduce or rise depending on the speed obtained.

Equipment

Meter stick, materials to make ramp (books), a toy car, a flat smooth surface, a weighing scale, and a stopwatch

Risk Assessment

A risk is a danger, hazard or exposure to peril. Risks can either be voluntary, involuntary, verifiable or statistically non-verifiable. Voluntary hazards involve tasks that one can undertake, such as ladder climbing, skydiving, car driving, racing, and motorcycle riding. Involuntary hazards happen to us without our knowledge and include impacts caused by naure like floods, lighting, fires, etc.

Statistically verifiable risks are the ones that can be determined through observation and are either involuntary or voluntary. They can be compared to other risks. Statistically non-verifiable hazards are involuntary dangers that entail limited information and mathematical expressions.

Friction resistance is one of the risk to be assessed. The friction force is a resistance of one body’s motion moving relative to another. This risk is controlled by smoothening the surface between the ramp and the flat surface. One can also use manila to reduce the risk.

Additionally, errors that could be human or systematic may occur, resulting in an incorrect investigation. These errors will be avoided by being careful while taking and recording measurements. Another risk is that of the toy car having less control. Less control happens when the toy moves at much higher speeds. The risk can be controlled by not attaining very steep slopes.

Variable Table

The controlled variables are the horizontal length covered, the toy’s mass, and the slope’s length. The friction resistance is ignored; thus, it is a controlled variable. The ramp’s height is increased at an equal interval, and hence it is an independent variable. The angle of deviation/elevation is an independent variable. Time is also a dependent variable.

The dependent variables will change in response to independent variables. Dependent variables are either measured or observed. An independent variable is what one can decide to change in research. A controlled variable is any parameter that is held constant or is limited in an experiment.

Method

Procedure

Select open space (5m) and place your ramp using the lab room materials. The ramp is created by stacking two books on top of each other. The transition between flat surface and ramp is made as smooth as possible using manila paper.Using the meter stick, mark the initial point at the ramp’s top and an endpoint around a meter beyond the ramp on the flat ground. The distance between the ramp’s end and stopping point is measured and written. Additionally, measure the starting point’s height above the surface and record it down.Place a masking tape marker where the ramp touches the floor and label it 0m.Take some practice runs with the cart. Ramp height adjustment or smoothening of the surface may be needed. The cart is needed to go at least 5.0m.Release the toy car from the top of the ramp and begin timing it at the 0m mark. Stop the timer at each marker. You will need to take three trial runs. Record your times in the data table.Add one more book to stack, making it three books to raise the ramp and repeat steps D and E. Repeat the same with four books and five books.Compute the average period for each meter marker and record it in the data table.

Results –Photos and Observations

Figure 2:  Two books ramp height set up

Figure 3: Experiment design diagram (final set up)

The time recorded is observed to decrease with the steepness of the slope. The slope increased with the addition of more books.

The toy car will move faster when there are five books and the slowest when there are two books. When the books were two, the time obtained was more than when the books were three, four or five. Hence, the speed when books are two is anticipated to be very small compared to when the five books are used. The deviation angle is slight for the two books and more prominent when the books are five.

h / l      = sin θ ……………………eqn 2

From equation 2, θ will increase as more books (h) are added since l is constant.

Results Table and Graph

Table1: Trial data

 trial 1trial 2trial 3avg. timespeed (m/s)2 books 7.210.129.628.980.5567928733books 6.36.567.166.6733330.7492507494books 5.125.525.65.4133330.923645325books 55.34.644.981.004016064

To obtain the speed, the following expression is used: Speed = distance /time

Graph 1: speed verse ramp height                            Graph 2: Time against ramp height

 Taking the mass of the toy as 500g and using the data on table one, we obtain kinetic energies as in table 2 below

Table 2: Kinetic energies  KE= ½ Mass *V2

Mass of toy  = 0.5kgspeed (m/s)K.E (J)2 books0.556792870.0775053books0.749250750.1403444books0.923645320.213285books1.004016060.252012

Graph 3: Kinetic energy against speed

Discussion

In graph 1, as ramp height increases, the toy car’s speed increases too. This means that the toy accelerates more when the deviation angle is larger than when it is small. For graph 2, the time is inversely proportional to ramp height. The time needed to cover the constant horizontal distance reduces as the ramp height is added. Hence, the deviation angle is also inversely proportional to time.

The gravitational pull acts more on a particle rolling down a ramp inclined at a steeper deviation angle, thus faster movement and acceleration.  In the case of dummies, it is explained that when particles are rolling down a steep plane like a ramp, a component of gravitational forces results in downward acceleration.

Figure 4: General Inclined particle – Dummy case

Neglecting the friction between the plane and the object, the force needed to move the body up an inclined plane can be obtained as

Fp = W h / l       = W sin α         = m ag sin α                           

Where

Fp = pulling force (N); W = m ag     = gravity force – or weight of body (N)

h = elevation (m, ft)      l = length (m, ft)

α = elevation angle (degrees) /deviation angle                 m = mass of body (kg,)

ag = acceleration of gravity

The force will increase as the angle of deviation increases from the equation above. At a constant horizontal distance, deviation becomes larger as the ramp height or elevation is added. Using figure 4 above, it can be argued that the inclination of a ramp towards gravitational pull direction will result in the object rolling at a speed that nears the total force. Therefore, an object on the ground encounters a continuous gravitational pull directed straight downwards. Thus, ramp experiments cannot measure the force of earth acceleration.

Conclusion

The degree of tilt or angle of deviation affects the toy car’s speed. The toy car’s speed increases with an increase in the deviation angle. The speed is directly proportional to ramp height and inversely proportional to the time taken at a constant distance. The angle of deviation increases with an increase in vertical height. The greater the inclination angle, the higher the speed.

Kinetic energies’ values by the cart at each ramp height are calculated for further correlation between deviation angle and speed.  As the ramp height and speed increased, so did the kinetic energy. When speed is doubled, the energy is expected to be fours times. When speed was doubled from our design experiment, the kinetic energy was not multiplied by four but by 3.25. This implies that some of the energy was lost in the experiment.  Some of the parameters that could have contributed to energy losses are friction resistance and air resistance. Some energy is needed to overcome the friction drag against a moving object, thus explaining why the energy is lost. Additionally, when the angle of deviation was increased, and the speed increased significantly, air drag by air molecules oppose the motion hence energy loss.

 Reducing friction and hence energy loss is done by lubricant application on the fine pores. Other means of reducing friction include polishing uneven surfaces and using ball bearings on rotational machines. Streamlining bodies of aeroplanes or cars reduce air drag. In our experiment, smoothening was applied.  

References

Pendrill, A. M., Ekström, P., Hansson, L., Mars, P., Ouattara, L., & Ryan, U. (2014). Motion on an inclined plane and the nature of science. Physics Education, 49(2), 180.

Wick, D. P., & Ramsdell, M. W. (2002). Modeling the motion of a toy car traveling on an arbitrarily shaped track. American Journal of Physics, 70(7), 670-679.