A sled whose total mass with cargo is 30.0 kg rests on ice. The coefficient of static friction is 0.20, and the coefficient of kinetic friction is 0.15. The sled is attached to a rope, horizontally, in which the tension force is slowly increased. How much tension force applied by the rope will cause the sled to start moving?
T=F(fr) =μ(s) •m•g
To determine the tension force required to cause the sled to start moving, we need to compare the force of static friction (maximum force before the sled starts moving) with the tension force applied by the rope.
The force of static friction can be calculated using the equation:
Fs = μs * N
where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force exerted on the sled.
The normal force N is equal to the weight of the sled, which can be calculated using the equation:
N = m * g
where m is the total mass of the sled with cargo (30.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Now, substituting the values into the equations:
N = 30.0 kg * 9.8 m/s² = 294 N
Fs = 0.20 * 294 N = 58.8 N
Therefore, the force of static friction is 58.8 N.
Since the tension force applied by the rope is the force required to overcome the static friction, the tension force required to start the sled moving is also 58.8 N.