Question

16. A uniform beam (8.0 m long with mass m = 40 kg) is pivoted at its lower end, as shown. It is in equilibrium when a mass M = 200 kg is attached to its upper end and a light spring ($k = 5000$ N/m) is fixed a distance $d = 5.0$ m along the beam. If $\theta = 50^\circ$, find the subsequent elongation of the spring $\Delta x$. M $\theta$ 17. A small stick ($m = 30$ g and $l = 15$ cm) is placed inside a smooth cylinder, as shown. If $R = 7.0$ cm, find the forces on the cylinder exerted by the stick. 2R 18. A uniform ladder of mass m and length L leans against a wall. The soap suds on the floor make it very slippery. If the only friction considered is that provided by the wall acting on the top end of the ladder with coefficient of static friction $\mu$, what is the minimum value of $\theta$ for the ladder not to slip? 19. What is the critical value of coefficient of static friction between the sphere and the surface of the incline for the sphere to remain in equilibrium?

          16. A uniform beam (8.0 m long with mass m = 40 kg) is pivoted at its lower end, as
shown. It is in equilibrium when a mass M = 200 kg is attached to its upper end
and a light spring ($k = 5000$ N/m) is fixed a distance $d = 5.0$ m along the beam. If
$\theta = 50^\circ$, find the subsequent elongation of the spring $\Delta x$.

M
$\theta$
17. A small stick ($m = 30$ g and $l = 15$ cm) is placed inside a smooth cylinder, as
shown. If $R = 7.0$ cm, find the forces on the cylinder exerted by the stick.

2R
18. A uniform ladder of mass m and length L leans against a wall. The soap suds on
the floor make it very slippery. If the only friction considered is that provided by
the wall acting on the top end of the ladder with coefficient of static friction $\mu$,
what is the minimum value of $\theta$ for the ladder not to slip?

19. What is the critical value of coefficient of static friction between the sphere and
the surface of the incline for the sphere to remain in equilibrium?

16. A uniform beam (8.0 m long with mass m = 40 kg) is pivoted at its lower end, as
shown. It is in equilibrium when a mass M = 200 kg is attached to its upper end
and a light spring (k = 5000 N/m) is fixed a distance d = 5.0 m along the beam. If
θ = 50^∘, find the subsequent elongation of the spring Δ x.

M
θ
17. A small stick (m = 30 g and l = 15 cm) is placed inside a smooth cylinder, as
shown. If R = 7.0 cm, find the forces on the cylinder exerted by the stick.

2R
18. A uniform ladder of mass m and length L leans against a wall. The soap suds on
the floor make it very slippery. If the only friction considered is that provided by
the wall acting on the top end of the ladder with coefficient of static friction μ,
what is the minimum value of θ for the ladder not to slip?

19. What is the critical value of coefficient of static friction between the sphere and
the surface of the incline for the sphere to remain in equilibrium?

Added by Miriam A.

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