a warehouse worker pulls on the handles of a 96.0 kg cart witha net force of 128N an angle of 55.0 degrees above the horizontal. Attached to the cart is a smaller cart having a mass of 72.0kg. What is the magnitude of the horizontal acceleration of the less massive cart?
Well, well, well, Mr. Warehouse Worker! Looks like you're giving that cart a good tug. Now, let's get down to business. The first thing we need to do is to break down the force into its horizontal and vertical components.
The horizontal component of the force is calculated by multiplying the net force by the cosine of the angle. So, F_horizontal = 128N * cos(55°). Can you calculate it for me? Don't worry, I won't clown around and make it too complicated!
Once you have the value for F_horizontal, you can use Newton's second law, F = m * a, where F is the force, m is the mass, and a is the acceleration. In this case, the mass is the smaller cart that the warehouse worker is trying to accelerate. So, plug in the mass of 72.0kg and solve for the acceleration.
And voila! You've got the magnitude of the horizontal acceleration of the less massive cart. You did an awesome job, my friend! Keep up the hard work, and remember, laughter is the best packing material in any warehouse!
To find the magnitude of the horizontal acceleration of the smaller cart, we need to analyze the forces acting on it.
First, let's break down the force applied by the warehouse worker into horizontal and vertical components. The horizontal component of the force can be calculated using the formula:
F_horizontal = F * cos(theta)
Where F is the net force applied by the warehouse worker, and theta is the angle above the horizontal. Substituting the given values:
F_horizontal = 128 N * cos(55.0 degrees)
Now we have the horizontal component of the force exerted by the warehouse worker. Since this force is causing the smaller cart to accelerate horizontally, by Newton's second law (F = ma), we have:
F_horizontal = m * a
Where m is the mass of the smaller cart, and a is the horizontal acceleration we want to find. Rearranging the formula:
a = F_horizontal / m
Substituting the known values:
a = (128 N * cos(55.0 degrees)) / 72.0 kg
Calculating this using a calculator:
a ≈ 1.29 m/s²
Therefore, the magnitude of the horizontal acceleration of the smaller cart is approximately 1.29 m/s².