Question

unit 2 exam mcq portion (10 question version) a block of mass m is accelerated across a rough surface by a force of magnitude f that is exerted at an angle φ with the horizontal, as shown above. the frictional force on the block exerted by the surface has magnitude f. 7. what is the acceleration of the block? (a) $\frac{f}{m}$ (b) $\frac{fcosphi}{m}$ (c) $\frac{f - f}{m}$ (d) $\frac{fcosphi - f}{m}$ (e) $\frac{fsinphi - mg}{m}$ 8. what is the coefficient of friction between the block and the surface? (a) $\frac{f}{mg}$ (b) $\frac{mg}{f}$ (c) $\frac{mg - fcosphi}{f}$ (d) $\frac{f}{mg - fcosphi}$ (e) $\frac{f}{mg - fsinphi}$ on a level horizontal table, a toy race car of mass m moves with constant speed v around a flat circular racetrack of radius r. 9. which of the following best represents the minimum coefficient of static friction required for the race car to continue to follow the circular path shown?

Explanation:

Step1: Analyze horizontal forces for block acceleration

According to Newton's second - law $F_{net}=ma$. The horizontal component of the applied force is $F\cos\phi$ and the frictional force is $f$. The net horizontal force is $F_{net,x}=F\cos\phi - f$. Then $F\cos\phi - f=ma$, so $a=\frac{F\cos\phi - f}{m}$.

Step2: Analyze normal force for coefficient of friction

The normal force $N$ on the block is given by the vertical - force balance. The vertical component of the applied force is $F\sin\phi$ and the weight is $mg$. So, $N + F\sin\phi=mg$, then $N = mg - F\sin\phi$. The frictional force $f=\mu N$, and the coefficient of friction $\mu=\frac{f}{N}=\frac{f}{mg - F\sin\phi}$.

Step3: Analyze centripetal force for car's friction

For the car moving in a circular path, the centripetal force $F_c=\frac{Mv^{2}}{R}$ is provided by the frictional force $F_f=\mu_sN$. On a horizontal surface, $N = Mg$. Setting $F_c = F_f$, we have $\frac{Mv^{2}}{R}=\mu_sMg$, so $\mu_s=\frac{v^{2}}{gR}$.

Answer:

1. D. $\frac{F\cos\phi - f}{m}$
2. E. $\frac{f}{mg - F\sin\phi}$
3. $\frac{v^{2}}{gR}$ (no options provided for question 9 in the answer - choice part of the response as they were not given in the problem statement for this sub - question)