Question$\qquad$ 3. An object of mass $m$ is released from rest on a surface with a circular cross-section of radius $r$. The coefficient of kinetic friction between the object and the surface of the arc is $\mu_{\mathrm{k}}$. The block slides through angle theta, reaching its lowest point, and then slides upwards through angle phi, coming to rest at point $P_{2}$. What is the work done by the force of friction on the block? a. $m g r\left(\cos \left(\theta_{1}\right)-\cos \left(\theta_{2}\right)\right)$ b. $m g r\left(\cos \left(\theta_{2}\right)-\cos \left(\theta_{1}\right)\right)$ c. $m g r\left(\cos \left(\theta_{1}\right)+\cos \left(\theta_{2}\right)\right)$ d. $m g r$ $\qquad$ 4. A woman runs up a flight of stairs. The gain in her gravitational potential energy is $U$. If she runs up the same stairs with twice the speed, what is her gain in potential energy? a. $U$ b. $2 U$ c. $\frac{1}{2} U$ d. $4 U$ 2