Calvin is pulling Hobbes on his sled with a force of 45 N [30o above the ground]. The mass of Hobbes
and the sled is 18 kg and the coefficient of friction between the sled and the ground is 0.25.
Determine a) the net force in the vertical.
in this case is the net force going to equal 0 ?
i got net force 176.4 N is that right? what i did was
fnet=ma
fnet= 18(9.8)
=176.4
See previous post: Fri, 10-23-15, 10:39 PM.
In this case, the net force in the vertical direction is not necessarily equal to zero. The net force is the vector sum of all the forces acting in the vertical direction.
To calculate the net force, you need to consider the force of gravity and the vertical component of the force Calvin is applying.
The force of gravity acting on Hobbes and the sled can be calculated using the equation Fgravity = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²). In this case, the force of gravity is Fgravity = 18 kg * 9.8 m/s² = 176.4 N.
The vertical component of the force Calvin is applying can be calculated by multiplying the total applied force by the cosine of the angle above the ground. In this case, the vertical component is Fapplied = 45 N * cos(30°) = 38.93 N.
Finally, the net force in the vertical direction can be calculated by finding the difference between the force of gravity and the vertical component of the applied force:
Net force (vertical) = Fgravity - Fapplied
= 176.4 N - 38.93 N
= 137.47 N.
So, the net force in the vertical direction is 137.47 N, not 0 N.
To determine the net force in the vertical direction, we need to consider all the forces acting in that direction.
1. The force due to gravity (weight): The weight of the sled and Hobbes is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity (which is approximately 9.8 m/s^2). In this case, the mass is 18 kg, so the weight is W = 18 kg * 9.8 m/s^2.
2. The vertical component of the force Calvin is exerting (45 N [30o above the ground]): Since the force is applied at an angle of 30 degrees above the ground, we need to find the vertical component of the force. This can be calculated using the formula F_vertical = F * sin(theta), where F is the given force and theta is the angle. In this case, F = 45 N and theta = 30 degrees.
3. The force of friction: The coefficient of friction (0.25) is given, and the force of friction can be determined using the formula F_friction = coefficient_of_friction * normal_force. The normal force is the force exerted by the ground on the sled and can be approximated to be equal to the weight (assuming the sled is not sinking into the ground). So, F_friction = 0.25 * W.
Now, to find the net force in the vertical direction, we add up all the forces acting in that direction:
Net force = (vertical component of the applied force) - (weight) - (force of friction)
Net force = (45 N * sin(30 degrees)) - (18 kg * 9.8 m/s^2) - (0.25 * 18 kg * 9.8 m/s^2)
You can now calculate the value of the net force by plugging in the numerical values and evaluating the expression.