A 5000kg truck is being pulled up a 15 degree ramp by a cable which is parallel to the surface of the ramp. If the coefficient of friction u between the wheels of the truck and the ramp is 0.100 and the truck is being pulled at a constant velocity, calculate the tension in the cable
See previous post.
To calculate the tension in the cable, we need to analyze the forces acting on the truck.
1. Weight force (Fg):
The weight force is the force due to gravity acting on the truck. It can be calculated using the formula Fg = m * g, where m is the mass of the truck (5000 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, Fg = 5000 kg * 9.8 m/s^2.
2. Normal force (Fn):
The normal force is the force exerted by the ramp on the truck, perpendicular to the surface of the ramp. It can be calculated using the formula Fn = m * g * cos(θ), where θ is the angle of the ramp (15 degrees). Therefore, Fn = 5000 kg * 9.8 m/s^2 * cos(15 degrees).
3. Frictional force (Ff):
The frictional force is the force opposing the motion of the truck. It can be calculated using the formula Ff = u * Fn, where u is the coefficient of friction (0.100) and Fn is the normal force. Therefore, Ff = 0.100 * Fn.
4. Tension force (Ft):
The tension force in the cable is the force pulling the truck up the ramp. Since the truck is being pulled at a constant velocity, the tension force and the frictional force must be equal in magnitude. Therefore, Ft = Ff.
Now we can calculate the tension in the cable (Ft). Let's substitute the values into the equations:
Fg = 5000 kg * 9.8 m/s^2
Fn = 5000 kg * 9.8 m/s^2 * cos(15 degrees)
Ff = 0.100 * Fn
Ft = Ff = 0.100 * Fn
By plugging in the values and solving the equations, we can find the tension in the cable.