A compact car can achieve a maximum acceleration of 3.2 m/s^2. If dice were hanging from the rearview mirror, what angle would they swing on?
Tsinα =ma
Tcosα =mg
tanα=a/g=3.2/9.8 = 0.33
α = 18°
To find the angle at which the dice would swing on, we need to consider the forces acting on them. When the car accelerates, a pseudo force (also known as the apparent force) is experienced by objects inside the car due to the car's acceleration.
The equation to calculate the pseudo force experienced by an object inside the car is:
Fpseudo = m * a
Where:
- Fpseudo is the pseudo force experienced by the object (in newtons)
- m is the mass of the object (in kilograms)
- a is the acceleration of the car (in meters per second squared)
Assuming the mass of each dice is 0.2 kg, we can now calculate the pseudo force. Given that the car's maximum acceleration is 3.2 m/s^2:
Fpseudo = 0.2 kg * 3.2 m/s^2 = 0.64 N
The force experienced by the dice is equal to the force of gravity acting on them:
Fgravity = m * g
Where:
- Fgravity is the force of gravity acting on the dice (in newtons)
- m is the mass of the dice (in kilograms)
- g is the acceleration due to gravity, approximately 9.8 m/s^2
Fgravity = 0.2 kg * 9.8 m/s^2 = 1.96 N
Now, we can find the angle at which the dice would swing on. This angle is determined by the ratio of the pseudo force to the force of gravity:
tan(θ) = (Fpseudo / Fgravity)
θ = arctan(Fpseudo / Fgravity)
θ ≈ arctan(0.64 N / 1.96 N)
Using a calculator to find the arctan, the angle θ is approximately 18.7 degrees.
So, if dice were hanging from the rearview mirror in a compact car with a maximum acceleration of 3.2 m/s^2, they would swing at an angle of approximately 18.7 degrees.