A large dam scraper , with a mass of 900kg , is used to build an earth dam by means of a winch system. The slope of the dam wall is 60° to the horizontal and is 18m long .The loading capacity of the dam scraper is 1,5m ^3 of soil and the density of the soil is 3200kg/m^3 . The tractive resistance of the dam scraper up the slope is 650N .calculate:

1.The tensile force in the cable of the winch to pull the loaded dam scraper up the slope.

component of weight down slope = m g sin 60

m = ( 900 + 3200*1.5 ) kg
g = 9.81 m/s^2 or whatever you use on your planet

Tension = 650 + m g sin 60

To calculate the tensile force in the cable of the winch, we need to consider the forces acting on the loaded dam scraper. There are two main forces to consider: the force due to the weight of the dam scraper and the force due to the tractive resistance.

1. Force due to the weight of the dam scraper:
The weight of the dam scraper can be calculated using the formula: weight = mass × gravitational acceleration.
Given that the mass of the dam scraper is 900 kg, and the gravitational acceleration is typically approximated to 9.8 m/s^2, we can calculate the weight:
weight = 900 kg × 9.8 m/s^2 = 8820 N (Newtons)

2. Force due to tractive resistance:
The tractive resistance of the dam scraper up the slope is given as 650 N.

Now, we need to calculate the component of the weight that acts parallel to the slope. This can be done using trigonometry. The slope of the dam wall is 60° to the horizontal, so the angle between the slope and the vertical is 90° - 60° = 30°.

The component of the weight parallel to the slope can be calculated using the formula: force_parallel = weight × cos(angle).
In this case, angle = 30°.

force_parallel = 8820 N × cos(30°) = 8820 N × 0.866 = 7633.32 N (approximately)

Finally, we can calculate the tensile force in the cable of the winch by adding the force due to tractive resistance to the force parallel to the slope:
tensile force = force_parallel + tractive resistance
tensile force = 7633.32 N + 650 N = 8283.32 N (approximately)

Therefore, the tensile force in the cable of the winch to pull the loaded dam scraper up the slope is approximately 8283.32 N.