Tension and other assorted fun

[bknice02]

1. A 52.0 kg person takes a nap in a (lightweight) backyard hammock. Both ropes supporting the hammock are at an angle of 14.9° above the horizontal. Find the tension in the ropes.

2. A backpack full of books weighing 52.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 155 N/m is attached to the backpack and pulled horizontally. (a) If the spring is pulled until it stretches 1.70 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table?

3. A box is placed on a conveyor belt that moves with a constant speed of 1.38 m/s. The coefficient of kinetic friction between the box and the belt is 0.920. (a) How long does it take before the box stops sliding relative to the belt? (in seconds) (b) How far has the box moved in this time? (in meters)


I don't expect to be given the answers, I just need to be pointed in the right direction

 

[zwtipp05]

Look at the resultant Forces

F=-kx

not much else I can help you with without you showing what you've done. then we can point out any problems in what you're doing.

 

[quicknote]

.

I would approach these questions by first identifying the relevant equations and principles that can be used to solve them. For the first question, the tension in the ropes can be found using the equation T = mg/cosθ, where T is the tension, m is the mass of the person, g is the acceleration due to gravity, and θ is the angle of the ropes. In this case, we know all the values except for T, so we can plug them in and solve for T.

For the second question, we can use the equation F = kx to find the force exerted by the spring, where F is the force, k is the force constant, and x is the displacement of the spring. We also know that this force is equal to the force of friction, so we can set up an equation to solve for the force of friction. We can then use the force of friction to find the coefficient of friction using the equation μ = Ff/N, where μ is the coefficient of friction, Ff is the force of friction, and N is the normal force.

For the third question, we can use the equation Ff = μN to find the force of friction between the box and the conveyor belt. We also know that the force of friction is equal to the net force acting on the box, which is equal to the mass of the box times its acceleration. We can then use the equation F = ma to find the acceleration of the box. Once we have the acceleration, we can use the equation vf = vi + at to find the time it takes for the box to stop moving relative to the belt. Finally, we can use the equation d = vit + 1/2at^2 to find the distance the box has moved in this time.