Question

Forces at Angles 1. How much of the applied force is perpendicular to the ground and parallel to the ground? 50 N 40" 2. In the following frictionless situation, find the acceleration of the following object. 40 N ------20 - 20 kg 3. A boy is pulling a 200 N sled across a frozen pond as shown. Find the acceleration of the sled if the force is 70 N and, b) the amount of total force that the ice has to supply to keep the sled from breaking through? 4. Find the acceleration of the shopping cart in the following situation. 50 N 30* 64 N b) How much force do the wheels feel in this situation?

Answer 1

(1) F = 50 N

$\Theta$ = 40 deg

Force applied perpendicular to the ground, Fy = F*sin$\Theta$

= 50 N * sin40 = 32.14 N (Answer)

Force applied parallel to the ground, Fx = F*cos$\Theta$

  = 50 N * cos40 = 38.20 N (Answer)

(2) In this case, F = 40 N

$\Theta$​​​​​​ = 20 deg

Surface is frictionless, so frictional force = 0

So, total force in the horizontal direction -

Fx = F*cos$\Theta$

= 40*cos20 = 37.59 N

Mass of the object, m = 20 kg

Hence, acceleration of the object, a = Fx / m

= 37.59 / 20 = 1.88 m/s^2 (Answer)