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Two wooden crates rest on top of one another. The smaller top crate has a mass of m1 = 15 kg and the larger bottom crate has a mass of m2 = 88 kg. There is NO friction between the crate and the floor, but the coefficient of static friction between the two crates is μs = 0.85 and the coefficient of kinetic friction between the two crates is μk = 0.66. A massless rope is attached to the lower crate to pull it horizontally to the right (which should be considered the positive direction for this problem).
1)
The rope is pulled with a tension T = 275 N (which is small enough that the top crate will not slide). What is the acceleration of the small crate?
m/s2
2)
In the previous situation, what is the frictional force the lower crate exerts on the upper crate?
N
3)
What is the maximum tension that the lower crate can be pulled at before the upper crate begins to slide?
N
4)
The tension is increased in the rope to 1220 N causing the boxes to accelerate faster and the top box to begin sliding. What is the acceleration of the upper crate?
m/s2
5)
As the upper crate slides, what is the acceleration of the lower crate?
m/s2
2.66
39.9
858.8
6.47
12.76
In a classic carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the "stick" to the wall so they do not slide down. In one ride, the radius of the cylindrical room is R = 6.7 m and the room spins with a frequency of 21.9 revolutions per minute.
1)
What is the speed of a person "stuck" to the wall?
m/s
2)
What is the normal force of the wall on a rider of m = 45 kg?
N
3)
What is the minimum coefficient of friction needed between the wall and the person?
4)
If a new person with mass 90 kg rides the ride, what minimum coefficient of friction between the wall and the person would be needed?
5)
Which of the following changes would decrease the coefficient of friction needed for this ride?
increasing the rider's mass
increasing the radius of the ride
increasing the speed of the ride
increasing the acceleration due to gravity (taking the ride to another planet)
6)
To be safe, the engineers making the ride want to be sure the normal force does not exceed 2.4 times each persons weight - and therefore adjust the frequency of revolution accordingly. What is the minimum coefficient of friction now needed?
15.3
1572
.280
.280
increasing the speed of the ride
.416
A box rests on top of a flat bed truck. The box has a mass of m = 21 kg. The coefficient of static friction between the box and truck is μs = 0.85 and the coefficient of kinetic friction between the box and truck is μk = 0.69.
1)
The truck accelerates from rest to vf = 15 m/s in t = 13 s (which is slow enough that the box will not slide). What is the acceleration of the box?
m/s2
2)
In the previous situation, what is the frictional force the truck exerts on the box?
N
3)
What is the maximum acceleration the truck can have before the box begins to slide?
m/s2
4)
Now the acceleration of the truck remains at that value, and the box begins to slide. What is the acceleration of the box?
m/s2
5)
With the box still on the truck, the truck attains its maximum velocity. As the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding?
m/s2
1.15
24.1
8.33
6.76
8.33
A block with mass m1 = 8.5 kg is on an incline with an angle θ = 30° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.27 and μs = 0.297.
1)
When there is no friction, what is the magnitude of the acceleration of the block?
m/s2
2)
Now with friction, what is the magnitude of the acceleration of the block after it begins to slide down the plane?
m/s2
3)
To keep the mass from sliding, a spring is attached. What is the minimum spring constant of the spring to keep the block from sliding if it extends x = 0.17 m from its unstretched length?
N/m
4)
Now a new block with mass m2 = 14.9 kg is attached to the first block. The new block is made of a different material and has a greater coefficient of static friction. What minimum value for the coefficient of static friction is needed between the new block and the plane to keep the system from accelerating?
4.90
2.6
119
.737
The two blocks shown above are sliding across a frictionless surface by a force F from the left. The two blocks are not attached but the coefficient of static friction between the two is μs = 0.38. The mass of the smaller block is m1 = 12 kg and the mass of the larger block is m2 = 87 kg.
1)
Which of the diagrams above best represents the free-body diagram for M2?
Type in the number below the correct diagram.
2)
What is the minimum force required to keep the smaller block from sliding down the larger block?
N
3)
Now let's say that the mass of the smaller block is m1 = 13 kg and the mass of the larger block is m2 = 80 kg. (All the other quantities in the problem remain the same.) What is the minimum force required to keep the smaller block from sliding down the larger block?
N
1: down arrow on the top of the box
352
390.0
