a mechanic uses a chain and bloc pulley to lift a 875-kg engine 4.0 m to the top of the garage. the downward force on the chain over the 4.0 m distance is 5.0 x 10^4 N.
a)calculate the work done in raseing the motor
b)how much useful work was done
c)what is the inefficiency of the chain and block pulley in raising the motor
To solve this problem, we'll need to use the basic principles of work and force.
a) To find the work done in raising the motor, we can use the formula:
Work = Force x distance
In this case, the force applied is the downward force on the chain, which is 5.0 x 10^4 N, and the distance traveled is 4.0 m. Plug in these values into the formula:
Work = (5.0 x 10^4 N) x (4.0 m)
Work = 2.0 x 10^5 N·m
Therefore, the work done in raising the motor is 2.0 x 10^5 N·m.
b) To determine the useful work done, we need to consider the work done against gravity. The useful work is the work done in raising the motor, so the answer remains the same as in part a, which is 2.0 x 10^5 N·m.
c) The inefficiency of the chain and block pulley can be calculated by finding the ratio of the useful work done to the total work done.
Efficiency = (Useful work / Total work) x 100%
In this case, the useful work is 2.0 x 10^5 N·m (as calculated in part b), and the total work done is also 2.0 x 10^5 N·m (as calculated in part a). Plug in these values into the formula:
Efficiency = (2.0 x 10^5 N·m / 2.0 x 10^5 N·m) x 100%
Efficiency = 100%
Therefore, the inefficiency of the chain and block pulley in raising the motor is 100%.
To solve this problem, we'll use the formulas for work and efficiency.
a) The work done in raising the motor can be calculated using the formula:
Work = Force x Distance
Work = 5.0 x 10^4 N x 4.0 m
Work = 2.0 x 10^5 N·m
b) To calculate the useful work, we need to find the force required to lift the engine. This can be done using the weight formula:
Weight = Mass x Gravity
Weight = 875 kg x 9.8 m/s^2
Weight = 8575 N
The useful work can be calculated as:
Useful Work = Force x Distance
Useful Work = 8575 N x 4.0 m
Useful Work = 34300 N·m
c) The inefficiency of the chain and block pulley can be calculated using the formula:
Efficiency = (Useful Work / Work) x 100
Efficiency = (34300 N·m / 2.0 x 10^5 N·m) x 100
Efficiency = 17%
Therefore, the inefficiency of the chain and block pulley in raising the motor is 17%.