Problem 35 An empty sled of mass 25 kg slides down a muddy hill with a constant speed of 2.4 m/s. The slope of the hill is inclined at an angle of 15º with the horizontal as shown in the figure above.
Part A Calculate the time it takes the sled to go 21 meters down the slope The velocity is constant so just divide 21 meters by 2.4 meters per second.
Part A Meters cancel out and were left with a unit of time. That’s exactly what we want!
Part B On the dot below that represents the sled, draw and label a free-body diagram for the sled as it slides down the slope.
Part BFirst, the weight force. Weight always pointsstraight down, even if the object is on a slope.
Part BNow the normal force. The normal force isalways perpendicular to the surface thatthe object is on.
Part BNow friction. Friction is the along thesurface the object is traveling on.
Part C Calculate the frictional force on the sled as it slides down the slope. Change the axis so that the weight force is off at an angle
Part C Now that the FBD is rotated, the legs of the triangle formed by the weight force are equal to the Normal and friction forces because the sled is in equilibrium.
Part C How to find the values of the normal and friction forces. (aka the legs of the triangle) Used 10 for gravityMAKE SUREYOURCALCULATOR ISIN DEGREES!!!
Part C We use sine because friction equals the side opposite to the angle. After250 N multiplying by the weight force (the hypotenuse) we see that the force by friction is 64.705 Newtons
Part D Calculate the coefficient of friction between the sled and the muddy surface of the slope. To find the coefficient of friction we use the FUN equation.
Part DCosine 15 degrees times the weightforce equals the normal force (theadjacent leg of the triangle) 250 N
Part D Now we can plug in numbers to the FUN equation. f = 64.705 N N = 241.481 NN N N N N N And solve for μ
Part E The sled reaches the bottom of the slope and continues on the horizontal ground. Assume the same coefficient of friction.
Part Ei. In terms of velocity and acceleration, describe the motion of the sled as it travels on the horizontal ground. • The acceleration of the sled is now negative, meaning the sled’s velocity is decreasing and it is slowing down.
Part Eii. On the axes below, sketch a graph of speed (v) versus time (t) for the sled. Include both the sled’s travel down the slope and across the horizontal ground. Clearly indicate with the symbol tιthe time at which the sled leaves the slope.
Part EThe velocity is constant at 2.4 meters per seconduntil the sled leaves the slope. After that it beginsdecreasing until velocity equals 0 and it stopsmoving.