a device has a 100g wooden shuttle that is pulled along a square woooden rail by an elastic band. the shuttle is released when the elastic band has 9.0 N tension at a 45 degree angle. what is the magnitude of the initial acceleration of the shuttle?
F=ma
What are the forces on the shuttle
a> gravity
b> rubber band. the force of gravity down the rail is mg*.707
9-0.1*9.8*.707=0.1*a
solve for a
thanks, how did you get the .707 though?
Well, it sounds like the wooden shuttle is in for quite a ride! Let's do a bit of physics clowning to find its initial acceleration.
First, we need to resolve the tension force into its horizontal and vertical components. Since the angle is 45 degrees, both components are equal to 9.0 N × sin(45°) = 6.4 N.
Now, we can use Newton's second law, F = ma, to find the acceleration. The net force acting on the wooden shuttle is the horizontal component of the tension force, which is 6.4 N. Since the mass of the shuttle is 100 g (or 0.1 kg), we can rearrange the formula to solve for acceleration:
acceleration = net force / mass = 6.4 N / 0.1 kg = 64 m/s².
So, it seems like this little wooden shuttle is off to a speedy start with an initial acceleration of 64 m/s². Hang on tight, things are about to get exciting!
To find the magnitude of the initial acceleration of the shuttle, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Step 1: Determine the net force acting on the shuttle.
The tension force applied by the elastic band is responsible for the acceleration of the shuttle. We can decompose the tension force into vertical and horizontal components. The vertical component does not contribute to the horizontal acceleration, so we only need to consider the horizontal component.
The horizontal component of the tension force can be found using trigonometry:
F_horizontal = F_tension * cos(θ)
F_tension = 9.0 N (given)
θ = 45° (given)
F_horizontal = 9.0 N * cos(45°)
Step 2: Calculate the mass of the shuttle.
Given that the mass of the shuttle is 100 g, we need to convert it to kilograms:
mass = 100 g = 0.1 kg
Step 3: Apply Newton's second law to find the acceleration.
Newton's second law states:
F = m * a
a = F / m
Since our net force acting on the shuttle is the horizontal component of the tension force, we can substitute this value into the equation:
a = F_horizontal / m
Plug in the values we found earlier:
a = (9.0 N * cos(45°)) / 0.1 kg
Now, calculate the magnitude of the initial acceleration of the shuttle.