What ramp angle would produce an acceleration of 2 m/s2 for a cart rolling down? Assume no friction and that the angle is measured with respect to the horizontal.

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Physics

23 November, 09:43

What ramp angle would produce an acceleration of 2 m/s2 for a cart rolling down? Assume no friction and that the angle is measured with respect to the horizontal.

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Emeline · Answer 1

From Newton's second law:

a = F/mass

Therefore, acceleration of an object rolling a ramp would be:

a = g (sin theta) - friction coefficient (g) (sin theta)

The negative sine is due to the kinetic energy opposing the gravity

We are given that the friction coefficient is zero, the g is a constant = 9.8 m/sec and the acceleration is 2 m/sec^2

Substituting in the equation, we get:

2 = 9.8 sin (theta)

sin (theta) = 0.20408

theta = 11.7757 degrees