2.3 Forces and Newton's laws

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Question 56

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}

[4]

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.

[2]

2.3 Forces and Newton's laws

Question 56

Show that:

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

[4]

[2]

2.3 Forces and Newton's laws

Question 56

Markscheme

2.3 Forces and Newton's laws

Question 56

Markscheme

2.3 Forces and Newton's laws

Question 56

2.3 Forces and Newton's laws Questions

2.3 Forces and Newton's laws

Question 56

2.3 Forces and Newton's laws Questions