A child pulls on a rope of of sled that is stuck in snow at an angle of 34° with respect to the horizonal. The mass of the sled is 15 kg. Determine the applied force needed to get the sled moving if the coefficient of static friction between the sled and snow is 0.12 [Hint: when caculatING the force of friction, there are two forces upward]
M*g = 15 * 9.8 = 147 N. = Wt. of sled.
Fn = 147 - F*sin34 = 147-0.56F = Normal force.
Fs = u*Fn = 0.12(147 - 0.56F) = 17.64 - 0.067F = Force of static friction.
F*Cos34 - Fs = M*a.
0.83F - (17.64-0.067F) = 15 * 0,
0.83F + 0.067F -17.64 = 0,
0.9F = 17.64,
F = 19.7 N. = Applied force.
To determine the applied force needed to get the sled moving, we need to consider the forces acting on the sled.
1. Start by identifying the forces involved:
- The force of gravity (mg): This force acts vertically downward and is given by the mass (m) of the sled multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²).
- The normal force (N): This force acts perpendicular to the surface and prevents the sled from sinking into the snow. It is equal in magnitude and opposite in direction to the vertical component of the force of gravity, so N = mg * cos(θ), where θ is the angle with respect to the horizontal.
- The force of friction (Ff): This force acts parallel to the surface and opposes the motion of the sled. It can be calculated using the coefficient of static friction (μs) multiplied by the normal force, so Ff = μs * N.
2. Determine the normal force:
The normal force is the force exerted by the surface on the sled and is equal to the vertical component of the force of gravity. In this case, N = mg * cos(θ) = 15 kg * 9.8 m/s² * cos(34°).
3. Calculate the force of friction:
The force of friction is given by Ff = μs * N, where the coefficient of static friction (μs) is 0.12. Substituting the value of N from step 2, we get Ff = 0.12 * N.
4. Calculate the applied force:
To get the sled moving, the applied force needs to overcome the force of static friction. Therefore, the applied force is equal in magnitude to the force of friction, but opposite in direction. So, the applied force is -Ff.
Let's calculate the values:
N = 15 kg * 9.8 m/s² * cos(34°)
Ff = 0.12 * N
Applied force = -Ff
Now, you can substitute the values into the equations to find the specific numerical solution.