A 1130-kg car is held in place by a light cable on a very smooth (frictionless) ramp (?Fig. E5.8?). The cable makes an angle of 31.0° above the sur-face of the ramp, and the ramp itself rises at 25.0° 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?
Solution 8E Step 1 of 3: . (a) Draw a free-body diagram for the car. Here, the x-axis is taken along the surface of ramp and y-axis as the perpendicular from the ramp surface. Step 2 of 3: (b) Find the tension in the cable. Let tension in the rope be ‘T’. Weight due to mass of the car, W= mg 2 Using m =1130 kg and g= 9.8m/s W=(1130 kg )(9.8m/s ) 2 W=11074 N Along the X-axis(horizontal component along ramp) T cos(31)- W sin (25)= 0 Substituting W=11074 N T cos(31)- (11074) sin (25)= 0 Solving for tension, T= 11074 sin (25) Cos (31) T= 5460 N Therefore, the tension on the cable is 5460N.