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

W = m*g = 5000kg * 9.8N/kg = 49,000 N.=

Weight of truck.

Fp = 49000*sin15 = 12,682 N. = Force
parallel to ramp.
Fv = 4900*cos15 = 47,330 N. = Force
perpendicular to the ramp.

Fk = u*Fv = 0.10 * 47,330 = 4733 N. =
Force of kinetic friction.

T-Fp-Fk = m*a
T-12682-4733 = m*0 = 0
T-17,415 = 0
T = 17,415 N. = Tension in rope.

Correction:

Fv = 49,000*cos15 = 47,330 N,

To calculate the tension in the cable, we need to analyze the forces acting on the truck.

1. First, let's calculate the force of gravity acting on the truck. The force of gravity can be calculated using the formula F = mg, 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, the force of gravity is F_gravity = 5000 kg * 9.8 m/s^2 = 49000 N.

2. Next, let's determine the force of friction acting on the truck. The force of friction can be calculated using the formula F_friction = u * F_normal, where u is the coefficient of friction (0.100) and F_normal is the normal force acting on the truck. The normal force can be calculated by decomposing the force of gravity into components parallel and perpendicular to the ramp. The component perpendicular to the ramp is equal to F_normal = mg * cos(θ), where θ is the angle of the ramp (15 degrees). Therefore, F_normal = 5000 kg * 9.8 m/s^2 * cos(15 degrees) ≈ 46926.13 N. Finally, the force of friction is F_friction = 0.100 * 46926.13 N ≈ 4692.61 N.

3. Since the truck is being pulled up the ramp at a constant velocity, the tension in the cable must be equal to the force required to overcome the force of friction and provide a net force of zero. Therefore, the tension in the cable is Tension = F_gravity + F_friction = 49000 N + 4692.61 N = 53792.61 N.

Hence, the tension in the cable is approximately 53792.61 N.