I cannot for the life of me solve D.86 or D.88 Elements of Mechaaics D.ss See as

Question

I cannot for the life of me solve D.86 or D.88

Elements of Mechaaics D.ss See aso E,0, M. A sled of mass 10 kg is pulled along a horizontal frictional witlh an applied force of 50N acting at an angl sied is moving in the forward direction, and the coefficient o the sled and the surface on which it rides is 0.01. It so happes thatin r face D- 370 ween l at the (a) start and (b) end of che 4-second interval D.86 See also D.STJ time interval, the sled advances a distance of 1om. Determine the speed of the sledt Two parents, walking side-by-side on a horizontal snowy plane, pull a sled on which their child rides. Together the child and the sled have mnssIf 25 kg The coefticient of kinetic friction acting between the sled and the ground is 0.2. The mom apple a constant force, = 40 N, at an angle of T/G rad above the horizontal. The dad, who is somewhat taller, pulls with constant force at /4 rad above " (a) Determine the force that the dad must apply in order that the sled move forwar (b) Determine how hard the dad must pull to get the sled "airborne" for an instant HINT: The normal force of contact between the ground and the sled vanishes when they D.87 Sec abo D.86. The family in the previous problem encounters a snowy slope inclined at angle /12 upward with te- spect to the horizontal. The mom maintains a con stant force, F 40 N, at an angle of T/6 rad above the slope, while the dad pulls with constant force at /4 rad above the slope 12 (a) Determine the force that the dad must apply in order that the sled move uniformly (b) Determine how hard the dad must pull to get the sled "airborne" for an instant D.88 See also E.43 Run-away truck beds are stretches of in creasingly soft sand found at the bottom of steeply inclined roadways, in which vehi- cles whose brakes have failed may be safely brought to rest In this case, the truck, of mass M, enters the bed at z =0, with speed 10 at some initial instant. Our model shall attribute the effect of the truck bogging down in the increasingly soft bed to a force of kinetic friction with increasing coefficient, viz., ik = T, where L a constant with dimensions of length. Once the truck comes to rest, it remains at rest, as the frictional force vanishes from that time onward. Ascertain the distance (into the bed) at which the truck stops. D.89 See also E.37, R.19.

Explanation / Answer

D.86 :

given M = 25 kg

uk = 0.2

Fm = 40 N, phi = pi/6 rad

Fd , theta = pi/4 rad

a. for uniform motion

form force balance

N + Fmsin(phi) + Fd*sin(theta) = Mg

and

Fmcos(phi) + Fd*cos(theta) = ukN = uk(Mg - Fm*sin(phi) - Fd*sin(theta))))

Fd = [uk*Mg - uk*Fm*sin(phi) - Fm*cos(phi)/[cos(theta) + uk*sin(theta) ]

Fd = 31.7103 N

b. for the sled to become airborne

N = 0

Fd = (Mg - Fm*sin(phi))/sin(tehta) = 318.55160492 N

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