Question

A bobsled is on an inclined sheet of ice that is frictionless. What must be the angle of the incline if the acceleration of the bobsled is 2.77m/s^2?

Answer 1

θ = 73.6º

Step-by-step explanation:

To solve this exercise, let's use Newton's second law. Let's set a reference system where the x-axis is parallel to the inclined plane

with trigonometry we can find the components of the weight

sin θ = Wₓ / W

cos θ= W_y / W

Wₓ = W sin θ

W_ = W cos θ

Y axis

N - W_y = 0

N = W_y

X axis

Wₓ - fr = m a

mg cos θ - fr = m a

indicate that friction is zero, fr = 0

cos θ = a / g

θ = cos⁻¹
`(a)/(g)`

let's calculate

θ = cos⁻¹
`(2.77)/(9.8)`

θ = 73.6º