You set up a ramp with a length of 1.15 m, raising one end to a height of 0.4 m. You then roll a 0.300 kg toy car down the ramp, starting at rest
a)What is the change in potential energy of the toy car rolling down this ramp?
b)If all of that energy is changed into kinetic energy, what will the final speed of the toy car be?
To calculate the change in potential energy (PE) of the toy car as it rolls down the ramp, we can use the formula:
PE = m * g * h
where m represents the mass of the toy car (0.300 kg), g represents the acceleration due to gravity (9.8 m/s²), and h represents the height of the ramp (0.4 m).
a) Calculating the change in potential energy:
PE = 0.300 kg * 9.8 m/s² * 0.4 m
PE = 0.1176 J
Therefore, the change in potential energy of the toy car rolling down the ramp is 0.1176 Joules.
b) If all of the potential energy is converted into kinetic energy (KE), we can equate the two using the formula:
PE = KE
Now, the formula for kinetic energy is given by:
KE = 0.5 * m * v²
where v represents the final speed of the toy car.
By setting PE equal to KE and rearranging the formula, we can solve for the final speed:
0.1176 J = 0.5 * 0.300 kg * v²
v² = (0.1176 J) / (0.5 * 0.300 kg)
v² ≈ 0.392 m²/s²
Taking the square root of both sides, we find:
v ≈ √(0.392 m²/s²)
v ≈ 0.626 m/s
Therefore, the final speed of the toy car rolling down the ramp will be approximately 0.626 m/s.