A researcher is hauling a seismic sensor of mass $m$ kg up a rough Martian slope inclined at an angle $θ\theta$ to the horizontal. The sensor is pulled by a light, inextensible cable which makes a constant acute angle $ϕ\phi$ with the slope. The cable remains taut as the sensor is hauled with a constant acceleration $\text{ m s}^{-2}$ up the slope. The coefficient of friction between the sensor and the slope is $μ\mu$ . The tension in the cable is $P$ Newtons.

Show that:

\frac{m(a + g \sin \theta + \mu g \cos \theta)}{\cos \phi + \mu \sin \phi}

In a trial run where $m = 12$ , $θ=20∘\theta = 20^{\circ}$ , $ϕ=15∘\phi = 15^{\circ}$ , and $P = 85$ , the sensor is found to remain stationary. The researcher uses these values in the formula from part (a) to estimate a value for $μ\mu$ . Explain why this estimate of $μ\mu$ may be incorrect.

Show that:

\frac{m(a + g \sin \theta + \mu g \cos \theta)}{\cos \phi + \mu \sin \phi}

Applications of Forces

Question 109

Markscheme

Applications of Forces

Question 109

Markscheme

Applications of Forces

Question 109

Applications of Forces Questions

Applications of Forces

Question 109

Applications of Forces Questions