Tension in a cable at an angle

[da5id2]

I'm having trouble finding what formula to use for this:

A tow truck is connected to a 1400 kg car by a cable that makes a 25 degree angle to the horizontal.

If the truck accelerates at 0.55 m/s^2, what is the magnitude of the cable tension? Neglect friction and the mass of the cable.

 

[tiny-tim]

Welcome to PF!

A tow truck is connected to a 1400 kg car by a cable that makes a 25 degree angle to the horizontal.

If the truck accelerates at 0.55 m/s^2, what is the magnitude of the cable tension? Neglect friction and the mass of the cable.

Hi da5id2! Welcome to PF!

The car obviously has the same acceleration as the truck, 0.55 m/s^2.

So use good ol' Newton's second law for the external forces on the car in the horizontal direction.

 

[baba89]

The formula that you would use for calculating tension in a cable at an angle is the law of cosines. This formula takes into account the angle at which the cable is pulling and the forces acting on the cable. In this scenario, the forces acting on the cable would be the weight of the car and the acceleration of the truck.

To use the law of cosines, you would need to know the length of the cable and the angle at which it is pulling. In this case, the length of the cable can be calculated using trigonometry and the given angle of 25 degrees. Once you have the length of the cable, you can plug it into the law of cosines along with the weight of the car and the acceleration of the truck to calculate the tension in the cable.

In this scenario, the tension in the cable would be equal to the weight of the car multiplied by the cosine of the angle, plus the mass of the car multiplied by the acceleration of the truck. So the formula would be T = (mg)cosθ + (ma).

Substituting the given values, we get T = (1400 kg x 9.8 m/s^2)cos25 + (1400 kg x 0.55 m/s^2) = 13653.6 N + 770 N = 14423.6 N.

Therefore, the magnitude of the cable tension in this scenario would be approximately 14,423.6 Newtons. It is important to note that this is the maximum tension in the cable and it may vary depending on the acceleration and angle of the cable.