Acceleration of Forces at Angles

[kcrox]

A clerk moves a box of cans down an aisle by
pulling on a strap attached to the box. The
clerk pulls with a force of 176.0 N at an angle
of 30.0◦ with the horizontal. The box has a
mass of 40.0 kg, and the coefficient of kinetic
friction between the box and floor is 0.520.
The acceleration of gravity is 9.81 m/s2 .
What is the acceleration of the box?
Answer in units of m/s2.

Okay, this should be a simple problem, but I don't understand what it means when it says 'with the horizontal' and how that would look on my FBD. Help me please?

 

[ideasrule]

"with the horizontal" should be "to the horizontal"--that is, she pulls at an angle that's 30 degrees above the horizontal.

 

[tomcue]

The phrase "with the horizontal" means that the angle at which the clerk is pulling the box is measured from the horizontal direction, or the ground. In this case, the angle is 30 degrees above the ground.

To solve this problem, we can use the formula for calculating the acceleration of an object: a = Fnet/m, where Fnet is the net force acting on the object and m is the mass of the object.

First, we need to find the net force acting on the box. This can be done by breaking down the force of 176.0 N into its components along the x and y axes. Using trigonometry, we can find that the x component of the force is 176.0 N * cos(30 degrees) = 152.4 N, and the y component is 176.0 N * sin(30 degrees) = 88.0 N.

Next, we can calculate the force of friction acting on the box by using the formula Ff = μmg, where μ is the coefficient of kinetic friction, m is the mass of the box, and g is the acceleration of gravity. Plugging in the given values, we get Ff = (0.520)(40.0 kg)(9.81 m/s^2) = 203.04 N.

Now, we can find the net force by subtracting the force of friction from the x component of the pulling force: Fnet = 152.4 N - 203.04 N = -50.64 N. Note that the negative sign indicates that the net force is acting in the opposite direction of the pulling force.

Finally, we can plug in the net force and mass values into the acceleration formula: a = (-50.64 N)/(40.0 kg) = -1.266 m/s^2. The negative sign indicates that the box is accelerating in the opposite direction of the pulling force, which makes sense since the force of friction is slowing it down.

So, the acceleration of the box is -1.266 m/s^2, or approximately -1.27 m/s^2. The negative sign can be dropped since it only indicates the direction of the acceleration.