A car with a weight of 15 000 N is being towed up a 20o slope at constant
velocity. Friction is negligible. The tow rope is rated at 6 000 N maximum tension.
a. Draw the free body diagram, by cleverly choosing the coordinate system. (5 marks)
b. Calculate the tension in the rope. (5 marks)
c. Assess if the rope provided for towing the car is sufficient. (1 marks)
free body should show mg downward, of which mgSinTheta is down the slope.
tension=mg*sinTheta In my head, the rope will hold.
a. To draw the free body diagram, we need to consider the different forces acting on the car. Since the car is being towed up a slope at constant velocity and friction is negligible, the forces we need to consider are the gravitational force (weight) and the tension in the tow rope.
Let's choose a coordinate system where the x-axis is parallel to the slope, pointing up the slope, and the y-axis is perpendicular to the slope, pointing perpendicularly away from the slope.
Now, let's draw the free body diagram:
- Gravitational force (weight) acts vertically downwards. We can represent it as a vector with magnitude 15,000 N pointing downwards.
- Tension in the tow rope acts along the slope. We can represent it as a vector with an unknown magnitude pointing up the slope. Since the car is moving at constant velocity, the magnitude of the tension force needs to balance out the gravitational force.
b. To calculate the tension in the rope, we need to consider the equilibrium condition. Since the car is moving at constant velocity up the slope, the sum of forces in the y-direction must be zero.
Since there is no vertical component of the gravitational force (weight), the tension force must balance out the vertical component. The vertical component of the weight can be calculated using trigonometry.
Vertical component of weight = weight * sin(angle)
In this case, the angle is given as 20 degrees.
Vertical component of weight = 15,000 N * sin(20°)
Now that we have the vertical component of the weight, it should equal the magnitude of the tension in the rope.
Tension in the rope = Vertical component of weight = 15,000 N * sin(20°)
c. To assess if the rope provided for towing the car is sufficient, we compare the calculated tension in the rope to the maximum tension the rope is rated for. If the calculated tension is less than or equal to the maximum tension, then the rope is sufficient.
So, compare the calculated tension to the maximum tension of the tow rope:
Calculated tension = 15,000 N * sin(20°)
If the calculated tension is less than or equal to 6,000 N, then the rope provided is sufficient.