How Hard Does The Surface Of The Ramp Push On The Car?

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A 1130-kg car is held in place by a light cable on a very smooth (frictionless) ramp. The cable makes an angle of
31.0°C  above the surface of the ramp, and the ramp itself rises at  25.0°C above the horizontal.

(a) Draw a free-body diagram for the car.

(b) Find the tension in the cable.

(c) How hard does the surface of the ramp push on the car?

Answer

A)

Choose x- and y-coordinates that are parallel and perpendicular to the ramp, respectively. Our sketch of the free-body diagram for the car and the chosen coordinate axes, is shown in the figure below. As we see, we have expressed the x- and y-components (in red) of the vertical weight w of the car and the tension T in the cable (in blue).

how hard does the surface of the ramp push on the car?

Result

A) Our choice of coordinate axes is made by talking the x-axis parallel to the ramp and the y-axis perpendicular to it. All the forces acting on the car are identified and decomposed along the established coordinate axes.

B) 5460 N.

C) 7224 N.

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