A machine with velocity ratio five was used to race a load of1.2kg mass through the height of 10meter,If the work done to race the load is 800J find the useful work done please help me to solve it
To solve this problem, we need to first calculate the effort force and the distance moved by the effort. Then, we can calculate the useful work done.
1. Calculate the effort force (F_e) using the formula for velocity ratio:
Velocity Ratio = Load Distance / Effort Distance
In this case, the velocity ratio is given as 5 and the load distance is 10 meters. Since the effort distance is not known, we can assign it a variable, let's say "d_e". Thus, the equation becomes:
5 = 10 meters / d_e
Now we can solve for d_e by rearranging the equation:
d_e = 10 meters / 5
d_e = 2 meters
So, the effort distance is 2 meters.
2. Calculate the effort force (F_e) using the following formula:
Effort Force (F_e) = Load Mass x Acceleration due to Gravity
Given that the load mass is 1.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the effort force:
F_e = 1.2 kg x 9.8 m/s^2
F_e = 11.76 N
Therefore, the effort force is 11.76 Newtons.
3. Calculate the useful work done (W_useful) using the following formula:
Useful Work Done (W_useful) = Effort Force x Effort Distance
Given that the effort force is 11.76 N and the effort distance is 2 meters, we can calculate the useful work done:
W_useful = 11.76 N x 2 meters
W_useful = 23.52 J
So, the useful work done is 23.52 Joules.