A dog sled is pulled at an angle of 30 degrees with the horizon using a tension of 450N. If the sled has a mass of 50kg, then find the recoil, forward force and acceleration (if any).
A military gun is mounted on a railroad car (m = 1400 kg) as shown in the figure below There is no frictional force on the car, the track is horizontal, and the car is initially at rest. The gun then fires a shell of mass 31 kg with a velocity of 285 m/s at an angle of 35° with respect to the horizontal. Find the recoil velocity of the car
Forward force = T•cosα
To find the recoil, forward force, and acceleration of the dog sled, we need to analyze the forces acting upon it.
First, let's consider the vertical forces. Since the sled is on a flat surface, the vertical component of the tension force is balanced by the weight of the sled:
Vertical Component of Tension = Weight of the Sled
The weight of the sled can be calculated using the formula: weight = mass × acceleration due to gravity.
Weight of the Sled = 50 kg × 9.8 m/s^2 = 490 N
Now, let's consider the horizontal forces. The horizontal component of the tension force provides the forward force:
Forward Force = Horizontal Component of Tension
The horizontal component of the tension force can be calculated using the formula: horizontal component = tension × cosine(angle).
Horizontal Component of Tension = 450 N × cos(30°) = 450 N × sqrt(3)/2 ≈ 389.71 N
The recoil force can be found by subtracting the forward force from the horizontal component of the tension:
Recoil Force = Horizontal Component of Tension - Forward Force
Recoil Force = 389.71 N - Forward Force
Finally, let's consider the acceleration of the sled. Since the dog sled is on a flat surface and the vertical forces are balanced, the net force acting on the sled in the horizontal direction is the forward force. Therefore, we can use Newton's second law:
Net Force = Mass × Acceleration
Forward Force = 50 kg × Acceleration
Now we can use the equations derived to find the values:
Recoil Force = 389.71 N - Forward Force
Forward Force = 50 kg × Acceleration
The values of the recoil force, forward force, and acceleration can be solved by solving these equations simultaneously.