A traveller is pulling a 55kg load at 150degrees with a force of 600N along a horizontal floor. If the coefficient of friction between the floor and the load is 0.3, find the acceleration of the load?
Can you explain the angle? Measured from what reference?
Unless otherwise stated, the angle is measure CCW from the +x-axis.
150o CCW = 30o N. of W.
Mg = 55 * 9.8 = 539 N. = Wt. of load = Normal force(Fn).
Fk = u*Fn = 0.3 * 539 = 161.7 N. = Force of kinetic friction.
F*Cos30-Fk = M*a.
600*Cos30 - 161.7 = 55*a,
a = ?
F*Cos30
Correction: M*g = 55 b* 9.8 = 539 N. = Wt. of load.
Fn = 539 - 600*sin30 = 239 N.
Fk = u*Fn = 0.3 * 239 = 71.7 N. = Force of kinetic friction.
F*Cos30-Fk = M*a.
600*Cos30-71.7 = 55*a.
a = ?
To find the acceleration of the load, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to calculate the net force acting on the load. The net force is the vector sum of all the forces acting on the load.
In this case, the only horizontal force acting on the load is the force applied by the traveller, which has a magnitude of 600N.
The force of friction opposing the motion of the load can be calculated using the equation:
Force of friction = coefficient of friction * normal force
The normal force is the vertical force exerted by the floor on the load. Since the floor is horizontal and the load is pulled at an angle, the normal force can be calculated as:
Normal force = weight of the load * cosine(angle)
The weight of the load can be calculated as:
Weight of the load = mass of the load * acceleration due to gravity
Given that the mass of the load is 55kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the load.
Finally, the net force acting on the load is the difference between the applied force and the force of friction:
Net force = applied force - force of friction
Once we have the net force, we can use Newton's second law to solve for the acceleration:
Net force = mass of the load * acceleration
Thus, the formula to find the acceleration is:
acceleration = (applied force - force of friction) / mass of the load
Plugging in the given values:
- Calculate the normal force: Normal force = (55 kg * 9.8 m/s^2) * cos(150 degrees)
- Calculate the force of friction: Force of friction = 0.3 * Normal force
- Calculate the net force: Net force = 600 N - Force of friction
- Calculate the acceleration: Acceleration = Net force / 55 kg
By following these steps and plugging in the given values, you should be able to find the acceleration of the load.