A simple pendulum is made by attaching a small cup of sand with a hole in the bottom of a 1.2 m long string. The pendulum is mounted on the back of a small motorized car. As the car drives forward, the pendulum swings from side to side and leaves a trail of sand (15 cm from bottom of wave to bottom of wave) How fast was car moving?
To determine the speed of the car, we need to use information about the pendulum's motion and the trail of sand it leaves behind.
First, let's calculate the period of the pendulum. The period is the time it takes for the pendulum to complete one full swing from side to side. For a simple pendulum, the period can be calculated using the formula:
T = 2π√(L/g),
where T is the period, L is the length of the string, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the length of the string is 1.2 m, we can substitute these values into the formula:
T = 2π√(1.2/9.8).
Next, we need to find the time it takes for the pendulum to swing from one side to the other. The time taken for one complete swing is equal to the period divided by two. So, the time for one swing, T₁, would be:
T₁ = T/2.
Now, we can find the speed of the car by considering the distance between the bottom points of two consecutive swings of the pendulum. Given that the distance is 15 cm (0.15 m), and the time for one swing is T₁, we can use the formula:
Speed = Distance / Time.
So, the speed of the car can be calculated as:
Speed = 0.15 m / T₁.
After substituting the value of T₁ from the earlier calculation, we can determine the speed of the car.