Get insightful responses to your questions quickly and easily on IDNLearn.com. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

4. A 5.00-kg sled starts at rest and accelerates down a 45.0° incline. The coefficient of
kinetic friction between the mass and the incline is .185.
a) What is the value of the of the acceleration of the sled


Sagot :

Answer: [tex]5.64\ m/s^2[/tex]

Explanation:

Given

mass of sled m=5 kg

Elevation [tex]\theta =45^{\circ}[/tex]

[tex]\mu _k=0.185[/tex] (coefficient of kinetic friction)

Friction will oppose the motion of the sled while sled weight sin component helps it to move down the incline

[tex]W\sin\theta-F_r=ma\\where\\W=weight(mg)\\F_r=Friction(\mu_kmg\cos\theta)\\a=acceleration[/tex]

Substituting values

[tex]mg\sin \theta-\mu_kmgcos\theta=ma\\g\sin \theta-\mu_kg\cos \theta=a\\a=g(\sin 45^{\circ}-0.185\times \cos 45^{\circ})\\a=5.64\ m/s^2[/tex]