A 6.1 kg object hangs at one end of a rope that is attached to a support on a railroad boxcar. When the car accelerates to the right, the rope makes an angle of 39 with the vertical. Find the acceleration of the car.
The acceleration due to gravity is 9.8 m/s^2.
The 6.1 kg object hangs at one end of a rope that is attached to a support on a railroad boxcar.
There is a force of gravitation that acts on the object and pulls it in a direction vertically downwards. The magnitude of the force of gravity acting on the object is 6.1*9.8 N.
When the railroad boxcar accelerates to the right there is another force exerted on the object. This is in a horizontal direction and has a magnitude of 6.1*A where A denotes the acceleration of the car.
The resultant force of gravity and that due to the acceleration of the boxcar is making the direction of the rope from which the object is hanged inclined to the vertical at an angle of 39 degrees.
tan 39 = A/9.8
=> A = 9.8* tan 39
=> A = 7.935 m/s^2
The rate at which the car accelerates is 7.935 m/s^2