Question

A horse is harnessed to a sled having a mass of 241 kg, including supplies. The horse must exert a force exceeding 1260 N at an angle of 30.3° (above the horizontal) in order to get the sled moving. Treat the sled as a point particle.

(a) Calculate the normal force (in N) on the sled when the magnitude of the applied force is 1260 N. (Enter the magnitude.) __N

(b) Find the coefficient of static friction between the sled and the ground beneath it.

(c) Find the static friction force (in N) when the horse is exerting a force of 6.30 ✕ 10² N on the sled at the same angle. (Enter the magnitude.) __N

Answer 1

(a)

$N +Fsinθ =mg \\ N= mg -Fsinθ \\ N = 241 \times 9.81 -1260 \times sin(30.3°) \\ N= 2364.21 -635.69 \\ N= 1728.52\;N$

(b) For static

$\sum fx = 0 \\ Fcosθ -f =0 \\ Fcosθ = \mu N \\ \mu = \frac{Fcosθ}{N} \\ \mu = \frac{1260 \times cos(30.3°)}{N} \\ \mu = \frac{1260 \times 0.86339 }{1728.52} \\ \mu = 0.629$

(c) If F = 630 N

$N = mg -Fsinθ \\ N = 241 \times 9.81 -630 \times sinθ \\ N = 2364.21 -317.84 \\ N = 2046.37 \;N \\ f_R = \mu N \\ f_R= 0.629 \times 2046.37 \\ f_R = 1287.16 \;N$