For the girl pulling a sled with a mass of 6.0 kg t the left with a force of 10.0 N at a 30.0° angle, we have:
a) The normal force acting on the sled is 294 N.
b) The acceleration of the sled is 1.2 m/s².
a) We can calculate the normal force acting on the sled, with the sum of all the forces acting in the vertical direction:
(1)
Where:
W: is the weight force or force of gravity = 58.8 N
: is the component of the applied force in the y-direction
N: is the normal force =?
The vertical component of the force () can be calculated as follows:
(2)
Where:
F: is the applied force = 10.0 N
θ: is the angle (with the horizontal) = 30.0°
By entering equation (2) into (1) we have:
Hence, the normal force acting on the sled is 294 N.
b) The acceleration of the sled can be found with the forces acting on the x-direction:
Where:
a: is the acceleration =?
m: is the mass = 6.0 kg
: is the component of the applied force in the x-direction = Fcos(θ)
: is the force of friction = 1.5 N (it is negative because is in the opposite direction of motion)
Therefore, the acceleration is:
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