Concept #1: Forces in Connected Objects

Practice: If the table below is frictionless, find the tension on each of the two cables (find the system’s acceleration first).

Example #1: More Connected Objects

Practice: If the table below is frictionless, calculate the system’s acceleration. Find the rope’s tension.

Example #2: More Connected Objects

Practice: If m_{1} = 5 kg, m_{2} = 3 kg, Θ_{1} = 37°, and Θ_{2} = 53°, find the magnitude and direction of the system’s acceleration.

Consider the figure given below. Mass M 1 = 15 kg is free-hanging, supported by the tension in the rope. The mass M2 = 5 kg is at rest on the surface, under the influence of static friction with a coefficient μs = 0.4, which is balancing the tension in the rope pulling it to the right. In order for the rope to connect the masses, it passes over a pulley with mass m = 100 g supported by a rope anchored to the ceiling. In order for this system to be in equilibrium, what must the tension in the rope supporting the pulley be? Assume that the rope holding the pulley is attached to the center of the pulley, allowing it to freely change its angle θ, and that both ropes are massless.

In the figure below, a cart is pushed with a force F. If the coefficient of static friction between the cart and the box is 0.45, what is the minimum value of F in order for the box to not slide down the front of the cart?

In the figure below, the two boxes are initially at rest when a crane lifts the pulley with a force F. What is the motion of each box if the force is equal to 110 N?

A box, mass m, hangs from the pulley system shown to the right. What is the tension in the rope that runs over the pulleys? (Assume the rope and pulleys are massless and frictionless.)
A) mg
B) mg/2
C) 2mg
D) mg/4
E) mg/6

A 5 kg box rests on top of a 10 kg box. The friction coefficients between the 10 kg box and the floor are μs1 = 0.4 and μk1 = 0.3, and the friction coefficients between the 10 kg box and the 5 kg box are μs2 = 0.35 and μk2 = 0.25. If a horizontal force of 50 N is applied on the 10 kg box, which of the following statements is true
A) There is a static friction force on the 10 kg box, but no friction force on the 5 kg box
B) There is a static friction force on the 10 kg box and a static friction force on the 5 kg box
C) There is a kinetic friction force on the 10 kg box and a static friction force on the 5 kg box
D) There is a kinetic friction force on the 10 kg box and a kinetic friction force on the 5 kg box

A 5 kg box rests on top of a 10 kg box. The friction coefficients between the 10 kg box and the floor are μs1 = 0.4 and μk1 = 0.3, and the friction coefficients between the 10 kg box and the 5 kg box are μs2 = 0.35 and μk2 = 0.25. A horizontal force, F, is applied on the 10 kg box. What is the minimum value of F required to start moving the boxes?
A) 29.4 N
B) 39.2 N
C) 44.1 N
D) 58.8 N

A 10.0 kg block on a table is connected by a string to a 63-kg mass, which is hanging over the edge of the table. Assuming that frictional forces may be neglected, what is the magnitude of acceleration of the 10.0 kg block when the other block is released?
A) 9.0 m/s2
B) 7.5 m/s2
C) 8.1 m/s2
D) 8.5 m/s2

A force F pulls three blocks with masses m 1, m2, and m3 along a surface as shown the the picture below. The coefficient of kinetic friction between the blocks and the surface is given by μ, the tension in the strings between the blocks are T1 and T2, and the acceleration of the blocks is a. The acceleration of gravity is g. What is a correct equation for the tension T2 between the blocks with masses m2 and m3?
1. T2 = m2 (μg − a) − T1
2. T2 = T1 + m2 (μg + a)
3. T2 = T1 − m2 (μg − a)
4. T2 = T1 + m2 (μg)
5. T2 = F + T1 − m2 (μg + a)
6. T2 = T1 − m2 (μg + a)
7. T2 = T1 + m2 (μa)
8. T2 = T1 − m2 (μg)
9. T2 = T1 − m2 (a − μg)
10. T2 = T1 − μm2g + F − m 2a

A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration that the truck can have if the crate is to stay in place?[A] 3.92 m/s2[B] 8.00 m/s2[C] 31.2 m/s2[D] 78.5 m/s2[E] 196 m/s2

Box A, 15 kg, rests on a frictionless horizontal surface connected to box B, 5.0 kg, by a string as shown in the diagram. What is the magnitude of box B’s acceleration?A) 0.75 m/s2B) 9.8 m/s2C) 2.5 m/s2D) 1.5 m/s2E) 3.3 m/s2

A 5 kg box rests on top of a 10 kg box. The friction coefficients between the 10 kg box and the floor are μs1 = 0.4 and μk1 = 0.3, and the friction coefficients between the 10 kg box and the 5 kg box are μs2 = 0.35 and μk2 = 0.25. If a horizontal force of 50 N is applied on the 10 kg box, draw a free body diagram for each box, with the appropriate values of each force.

In the figure below, two masses, each 150 kg, are NOT at rest and are attached to each other by thin unstretchable cable. Find the acceleration of this system of masses and cable. The angle of the ramp is as shown in the figure. (Hint: Draw a free-body diagram for each mass) Find the magnitude and direction of the acceleration of the system if the coefficient of friction between block and ramp is 0.

In the figure below, two masses, each 150 kg, are NOT at rest and are attached to each other by thin unstretchable cable. Find the acceleration of this system of masses and cable. The angle of the ramp is as shown in the figure. (Hint; Draw a free body diagram for each mass) Find the magnitude and direction if the coefficient of friction is 0.100.