A sailor pushes a 195.0 kg crate up a ramp that is 2.00 m high and 6.00 m long onto the deck of a ship. He exerts a 750.0 N force parallel to the ramp. What is the mechanical advantage of the ramp? What is the efficiency of the ramp?
To determine the mechanical advantage of the ramp, we need to understand what it means. Mechanical advantage (MA) is the ratio of the output force to the input force required to complete a task.
In this case, the input force is the force exerted by the sailor, which is 750.0 N. The output force is the weight of the crate, which can be calculated as the mass multiplied by the gravitational acceleration (9.8 m/s^2), so the weight of the crate is (195.0 kg) * (9.8 m/s^2) = 1911 N.
Now, we can determine the mechanical advantage of the ramp:
MA = output force / input force
MA = 1911 N / 750.0 N
MA ≈ 2.548
Therefore, the mechanical advantage of the ramp is approximately 2.548.
To determine the efficiency of the ramp, we need to know the work done by the sailor and the work done against gravity.
The work done by the sailor is given by the equation:
Work = force x distance
The force exerted by the sailor is 750.0 N, and the distance he pushes the crate is 6.00 m. So the work done by the sailor is:
Work = 750.0 N * 6.00 m
Work = 4500 J
The work done against gravity is given by:
Work = force x distance
The force here is the weight of the crate, 1911 N, and the distance is the height of the ramp, 2.00 m. So the work done against gravity is:
Work = 1911 N * 2.00 m
Work = 3822 J
Now, we can determine the efficiency of the ramp:
Efficiency = (useful work output / total work input) x 100%
Since the useful work output is the work done by the sailor and the total work input is the sum of the work done by the sailor and the work done against gravity, the efficiency is:
Efficiency = (4500 J / (4500 J + 3822 J)) x 100%
Efficiency ≈ 54.080%
Therefore, the efficiency of the ramp is approximately 54.080%.