A car is towing a boat on a trailer. The driver starts from rest and accelerates to a velocity of +14 m/s in a time of 25 s. The combined mass of the boat and trailer is 401 kg. The frictional force acting on the trailer can be ignored. What is the tension in the hitch that connects the trailer to the car?
I have been trying to work out this problem for like 30 minutes. I've come up with 7859.6, 5894.7, and 3929.8 All of which haven't worked...help?!
v=at =>
a=v/t=14/25=0.56 m/s²
F=ma=401•0.56 = 226.56 N
Well, it sounds like you're really towing the line with this problem! Let's give it a shot and see if we can steer in the right direction!
To find the tension in the hitch, we can start by using Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force is the tension in the hitch.
First, let's calculate the acceleration of the car. We can use the equation:
acceleration = (final velocity - initial velocity) / time
acceleration = (14 m/s - 0 m/s) / 25 s
acceleration = 0.56 m/s^2
Now, to find the tension in the hitch, we can use the equation:
tension = mass × acceleration
tension = 401 kg × 0.56 m/s^2
tension = 224.56 N
So, the tension in the hitch that connects the trailer to the car is approximately 224.56 N.
Don't worry if it took you a while to work this out. Sometimes these problems can be a real drag!
To find the tension in the hitch that connects the trailer to the car, 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.
In this case, the net force is the tension in the hitch, and the acceleration is the acceleration of the car and the trailer combined. We need to calculate the acceleration first.
Given:
- Initial velocity of the car and the trailer, u = 0 m/s
- Final velocity of the car and the trailer, v = +14 m/s
- Time taken to reach the final velocity, t = 25 s
- Combined mass of the boat and trailer, m = 401 kg
First, we can calculate the acceleration using the formula:
acceleration (a) = (change in velocity) / time
change in velocity = final velocity - initial velocity
a = (v - u) / t
a = (14 m/s - 0 m/s) / 25 s
a = 0.56 m/s^2
Now that we have the acceleration, we can calculate the tension in the hitch using Newton's second law:
Tension = mass * acceleration
Tension = m * a
Tension = 401 kg * 0.56 m/s^2
Tension = 224.56 N
So, the tension in the hitch that connects the trailer to the car is approximately 224.56 N.