Question

A 1,126 kg car is held in place by a light cable on a very smooth (frictionless) ramp. The cable makes an angle of 36 degrees above the surface of the ramp, and the ramp itself rises at 26 degrees above the horizontal. How hard does the surface of the ramp push on the car? Use 9.80 m/s2 for the acceleration due to gravity.

Answer 1

Answer:

the push on the surface is equal to 6405.94 N

Explanation:

given,

mass of car = 1,126 Kg

cable makes an angle above the surface of ramp = 36°

angle of the ramp = 26°

acceleration due to gravity = 9.8 m/s²

to calculate the push on the ramp writing forces in vertical direction

N + T sin 36° - mg cos 26° = 0

N = mg cos 26° - T  sin 36°

N = 1126 × 9.81 × 0.898 - T × 0.587.................(1)

now writing equation in horizontal direction

mg sin 26° - T cos 36° = 0

$T =\dfrac{mgsin 26^0}{cos 36^0}$

$T =\dfrac{1126\times 9.81\times sin 26^0}{cos 36^0}$

T = 5985.38 N

from equation (1)

N = 1126 × 9.81 × 0.898 -5985.38× 0.587

   = 6405.94 N

hence, the push on the surface is equal to 6405.94 N