Final answer:
Most gasoline engines in today's automobiles are belt-driven, with the crankshaft being timed to the camshaft by means of a belt. Starting from rest, if it takes 0.032 s for a crankshaft with a radius of 4.25 cm to reach 1050 rpm, the angular acceleration of the crankshaft can be calculated as approximately 1106.3 rad/s².
Step-by-step explanation:
Most gasoline engines in today's automobiles are belt-driven, meaning that the crankshaft, which rotates and drives the pistons, is timed to the camshaft by means of a belt. Starting from rest, if it takes 0.032 s for a crankshaft with radius 4.25 cm to reach 1050 rpm and the belt does not stretch or slip, we can calculate the angular acceleration of the crankshaft.
The formula to calculate angular acceleration is:
angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω0)) / time (t)
In this case, the initial angular velocity (ω0) is 0 rpm, the final angular velocity (ω) is 1050 rpm, and the time (t) is 0.032 s.
Converting the angular velocities to radians per second:
1 rpm = 2π/60 rad/s
Initial angular velocity (ω0) = 0 rpm = 0 rad/s
Final angular velocity (ω) = 1050 rpm = (1050 * 2π/60) rad/s
Now we can substitute these values into the formula:
angular acceleration (α) = ((1050 * 2π/60) - 0) / 0.032
Simplifying the equation gives:
angular acceleration (α) = (105π/3) rad/s²
Therefore, the angular acceleration of the crankshaft is approximately 1106.3 rad/s².
Qn : Most gasoline engines in today's automobiles are belt driven. This means that the crankshaft, a rod which rotates and drives the pistons, is timed to the camshaft, the mechanism which actuates the vales, by means of a belt. Starting from rest, assume it takes t = 0.0540 s for a crankshaft with a radius of 4.25 cm to reach 1550 rpm. If the belt doesn't stretch or slip, calculate the angular acceleration of the larger camshaft, which as a radius of 8.50 cm, during this time period.